Abstract

A method is proposed to estimate the size distribution of nearly spherical metallic nanoparticles (NPs) from optical extinction spectroscopy (OES) measurements based on Mie’s theory and an optimization algorithm. The described method is compared against two of the most widely used techniques for the task: transmission electron microscopy (TEM) and small-angle x-ray scattering (SAXS). The size distribution of Au and Cu NPs, obtained by ion implantation in silica and a subsequent thermal annealing in air, was determined by TEM, grazing-incidence SAXS (GISAXS) geometry, and our method, and the average radius obtained by all the three techniques was almost the same for the two studied metals. Concerning the radius dispersion (RD), OES and GISAXS give very similar results, while TEM considerably underestimates the RD of the distribution.

© 2009 Optical Society of America

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2008

M. V Roldán, L. B. Scaffardi, O. de Sanctis, and N. Pellegri, “Optical properties and extinction spectroscopy to characterize the synthesis of amine capped silver nanoparticles,” Mater. Chem. Phys. 112, 984-990 (2008).
[CrossRef]

O. Peña, U. Pal, L. Rodríguez-Fernández, and A. Crespo-Sosa, “Linear optical response of metallic nanoshells in different dielectric media,” J. Opt. Soc. Am. B 25, 1371-1379(2008).
[CrossRef]

2006

S. Eustis and M. A. El-Sayed, “Determination of the aspect ratio statistical distribution of gold nanorods in solution from a theoretical fit of the observed inhomogeneously broadened longitudinal plasmon resonance absorption spectrum,” J. Appl. Phys. 100, 044324 (2006).
[CrossRef]

2005

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158-163 (2005).
[CrossRef]

C. Sünnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301-304 (2005).
[CrossRef]

2003

2002

R. Lazzari, “IsGISAXS: a program for grazing-incidence small-angle x-ray scattering analysis of supported islands,” J. Appl. Crystallogr. 35, 406-421 (2002).
[CrossRef]

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

2001

J. Yguerabide and E. E. Yguerabide, “Resonance light scattering particles as ultrasensitive labels for detection of analytes in a wide range of applications,” J. Cell. Biochem. Suppl. 84, 71-81 (2001).
[CrossRef]

F. Tihay, G. M. Pourroy, A. C. Roger, and A. Kienneman, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Appl. Catal. A 206, 29-42 (2001).
[CrossRef]

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

2000

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

F. Gonella, “Nanoparticle formation in silicate glasses by ion-beam-based methods,” Nucl. Instrum. Methods Phys. Res. Sect. B 166, 831-839 (2000).
[CrossRef]

1998

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

1997

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550-560 (1997).
[CrossRef]

1996

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

1995

R. H. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Statist. Comput. 16, 1190-1208 (1995).
[CrossRef]

1987

U. Kreibig, B. Schmitz, and H. D. Breuer, “Separation of plasmon-polariton modes of small metal particles,” Phys. Rev. B 36, 5027-5030 (1987).
[CrossRef]

1980

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comput. 35, 773-782 (1980).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Alivisatos, A. P.

C. Sünnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301-304 (2005).
[CrossRef]

Arnold, G. W.

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

Battaglin, G.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Borsella, E.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

Breuer, H. D.

U. Kreibig, B. Schmitz, and H. D. Breuer, “Separation of plasmon-polariton modes of small metal particles,” Phys. Rev. B 36, 5027-5030 (1987).
[CrossRef]

Budai, J. D.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Byrd, R. H.

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550-560 (1997).
[CrossRef]

R. H. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Statist. Comput. 16, 1190-1208 (1995).
[CrossRef]

Cattaruzza, E.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

Cheang-Wong, J. C.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Crespo-Sosa, A.

O. Peña, U. Pal, L. Rodríguez-Fernández, and A. Crespo-Sosa, “Linear optical response of metallic nanoshells in different dielectric media,” J. Opt. Soc. Am. B 25, 1371-1379(2008).
[CrossRef]

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

D'Acapito, F.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

de Sanctis, O.

M. V Roldán, L. B. Scaffardi, O. de Sanctis, and N. Pellegri, “Optical properties and extinction spectroscopy to characterize the synthesis of amine capped silver nanoparticles,” Mater. Chem. Phys. 112, 984-990 (2008).
[CrossRef]

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158-163 (2005).
[CrossRef]

El-Sayed, M. A.

S. Eustis and M. A. El-Sayed, “Determination of the aspect ratio statistical distribution of gold nanorods in solution from a theoretical fit of the observed inhomogeneously broadened longitudinal plasmon resonance absorption spectrum,” J. Appl. Phys. 100, 044324 (2006).
[CrossRef]

Eustis, S.

S. Eustis and M. A. El-Sayed, “Determination of the aspect ratio statistical distribution of gold nanorods in solution from a theoretical fit of the observed inhomogeneously broadened longitudinal plasmon resonance absorption spectrum,” J. Appl. Phys. 100, 044324 (2006).
[CrossRef]

Franzo, G.

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

Garcia, M. A.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

Gonella, F.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

F. Gonella, “Nanoparticle formation in silicate glasses by ion-beam-based methods,” Nucl. Instrum. Methods Phys. Res. Sect. B 166, 831-839 (2000).
[CrossRef]

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

Haglund, R.

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

Hembree, D. J.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Henderson, D. O.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Hernández, J. M.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kienneman, A.

F. Tihay, G. M. Pourroy, A. C. Roger, and A. Kienneman, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Appl. Catal. A 206, 29-42 (2001).
[CrossRef]

Kreibig, U.

U. Kreibig, B. Schmitz, and H. D. Breuer, “Separation of plasmon-polariton modes of small metal particles,” Phys. Rev. B 36, 5027-5030 (1987).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Lazzari, R.

R. Lazzari, “IsGISAXS: a program for grazing-incidence small-angle x-ray scattering analysis of supported islands,” J. Appl. Crystallogr. 35, 406-421 (2002).
[CrossRef]

Lu, P.

R. H. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Statist. Comput. 16, 1190-1208 (1995).
[CrossRef]

Mattei, G.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

Maurizio, C.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

Mazzoldi, P.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

Mazzoleni, C.

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

Meldrum, A.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Muñoz, E.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

Negro, L. D.

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

Nocedal, J.

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550-560 (1997).
[CrossRef]

R. H. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Statist. Comput. 16, 1190-1208 (1995).
[CrossRef]

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comput. 35, 773-782 (1980).
[CrossRef]

Oliver, A.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

Pal, U.

Pavesi, L.

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

Pellegri, N.

M. V Roldán, L. B. Scaffardi, O. de Sanctis, and N. Pellegri, “Optical properties and extinction spectroscopy to characterize the synthesis of amine capped silver nanoparticles,” Mater. Chem. Phys. 112, 984-990 (2008).
[CrossRef]

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158-163 (2005).
[CrossRef]

Peña, O.

Pourroy, G. M.

F. Tihay, G. M. Pourroy, A. C. Roger, and A. Kienneman, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Appl. Catal. A 206, 29-42 (2001).
[CrossRef]

Prawer, S.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Priolo, F.

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

Quaranta, A.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

Rodríguez-Fernández, L.

O. Peña, U. Pal, L. Rodríguez-Fernández, and A. Crespo-Sosa, “Linear optical response of metallic nanoshells in different dielectric media,” J. Opt. Soc. Am. B 25, 1371-1379(2008).
[CrossRef]

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

Roger, A. C.

F. Tihay, G. M. Pourroy, A. C. Roger, and A. Kienneman, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Appl. Catal. A 206, 29-42 (2001).
[CrossRef]

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A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

Roldán, M. V

M. V Roldán, L. B. Scaffardi, O. de Sanctis, and N. Pellegri, “Optical properties and extinction spectroscopy to characterize the synthesis of amine capped silver nanoparticles,” Mater. Chem. Phys. 112, 984-990 (2008).
[CrossRef]

Scaffardi, L. B.

M. V Roldán, L. B. Scaffardi, O. de Sanctis, and N. Pellegri, “Optical properties and extinction spectroscopy to characterize the synthesis of amine capped silver nanoparticles,” Mater. Chem. Phys. 112, 984-990 (2008).
[CrossRef]

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158-163 (2005).
[CrossRef]

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U. Kreibig, B. Schmitz, and H. D. Breuer, “Separation of plasmon-polariton modes of small metal particles,” Phys. Rev. B 36, 5027-5030 (1987).
[CrossRef]

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C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

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C. Sünnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301-304 (2005).
[CrossRef]

Tihay, F.

F. Tihay, G. M. Pourroy, A. C. Roger, and A. Kienneman, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Appl. Catal. A 206, 29-42 (2001).
[CrossRef]

Tocho, J. O.

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158-163 (2005).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

White, C. W.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Withrow, S. P.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Yang, W.

Yguerabide, E. E.

J. Yguerabide and E. E. Yguerabide, “Resonance light scattering particles as ultrasensitive labels for detection of analytes in a wide range of applications,” J. Cell. Biochem. Suppl. 84, 71-81 (2001).
[CrossRef]

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J. Yguerabide and E. E. Yguerabide, “Resonance light scattering particles as ultrasensitive labels for detection of analytes in a wide range of applications,” J. Cell. Biochem. Suppl. 84, 71-81 (2001).
[CrossRef]

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C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550-560 (1997).
[CrossRef]

Zhu, J. G.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

Zuhr, R. A.

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

ACM Trans. Math. Softw.

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM Trans. Math. Softw. 23, 550-560 (1997).
[CrossRef]

Appl. Catal. A

F. Tihay, G. M. Pourroy, A. C. Roger, and A. Kienneman, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Appl. Catal. A 206, 29-42 (2001).
[CrossRef]

Appl. Opt.

Comput. Phys. Commun.

O. Peña and U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” submitted to Comput. Phys. Commun.

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R. Lazzari, “IsGISAXS: a program for grazing-incidence small-angle x-ray scattering analysis of supported islands,” J. Appl. Crystallogr. 35, 406-421 (2002).
[CrossRef]

J. Appl. Phys.

E. Borsella, M. A. Garcia, G. Mattei, C. Maurizio, P. Mazzoldi, E. Cattaruzza, F. Gonella, G. Battaglin, A. Quaranta, and F. D'Acapito, “Synthesis of GaN quantum dots by ion implantation in dielectrics,” J. Appl. Phys. 90, 4467-4473 (2001).
[CrossRef]

S. Eustis and M. A. El-Sayed, “Determination of the aspect ratio statistical distribution of gold nanorods in solution from a theoretical fit of the observed inhomogeneously broadened longitudinal plasmon resonance absorption spectrum,” J. Appl. Phys. 100, 044324 (2006).
[CrossRef]

J. Cell. Biochem. Suppl.

J. Yguerabide and E. E. Yguerabide, “Resonance light scattering particles as ultrasensitive labels for detection of analytes in a wide range of applications,” J. Cell. Biochem. Suppl. 84, 71-81 (2001).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. Haglund, Jr., “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” J. Nonlinear Opt. Phys. Mater. 5, 285-330 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Mater. Chem. Phys.

M. V Roldán, L. B. Scaffardi, O. de Sanctis, and N. Pellegri, “Optical properties and extinction spectroscopy to characterize the synthesis of amine capped silver nanoparticles,” Mater. Chem. Phys. 112, 984-990 (2008).
[CrossRef]

Math. Comput.

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comput. 35, 773-782 (1980).
[CrossRef]

Nano Lett.

C. Sünnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301-304 (2005).
[CrossRef]

Nanotechnology

L. B. Scaffardi, N. Pellegri, O. de Sanctis, and J. O. Tocho, “Sizing gold nanoparticles by optical extinction spectroscopy,” Nanotechnology 16, 158-163 (2005).
[CrossRef]

Nature

L. Pavesi, L. D. Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444(2000).
[CrossRef] [PubMed]

Nucl. Instrum. Methods Phys. Res. Sect. B

C. W. White, J. D. Budai, S. P. Withrow, J. G. Zhu, E. Souder, R. A. Zuhr, A. Meldrum, D. J. Hembree, Jr., D. O. Henderson, and S. Prawer, “Encapsulated semiconductor nanocrystals formed in insulators by ion beam synthesis,” Nucl. Instrum. Methods Phys. Res. Sect. B 141, 228-240 (1998).
[CrossRef]

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, and E. Muñoz, “Metallic nanoparticle formation in ion-implanted silica after thermal annealing in reducing or oxidizing atmospheres,” Nucl. Instrum. Methods Phys. Res. Sect. B 191, 333-336(2002).
[CrossRef]

F. Gonella, “Nanoparticle formation in silicate glasses by ion-beam-based methods,” Nucl. Instrum. Methods Phys. Res. Sect. B 166, 831-839 (2000).
[CrossRef]

Phys. Rev. B

U. Kreibig, B. Schmitz, and H. D. Breuer, “Separation of plasmon-polariton modes of small metal particles,” Phys. Rev. B 36, 5027-5030 (1987).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Depth profile distributions obtained for (a) Au and (b) Cu from fitting the RBS spectra. The continuous curves (red) correspond to best fitting to experimental data assuming Gaussian functions.

Fig. 2
Fig. 2

Low magnification TEM micrographs obtained for (a) Au and (b) Cu NPs and (c) and (d) their corresponding probability histograms, respectively, obtained from the analysis of TEM images.

Fig. 3
Fig. 3

Experimental GISAXS intensity profiles (symbols) and best fit to experimental data (continuous curves) for (a) Au and (b) Cu adjusted considering spherical NPs with a normal distribution of radii. The curves are shifted by increasing powers of 10 for clarity. The α f value for each profile is indicated in the figure.

Fig. 4
Fig. 4

Fitting the OES spectra for (a) Au and (b) Cu, showing that an excellent agreement is obtained between the experimental spectra (continuous black curves) and the simulated ones (dotted red curves) for the given values of AR and RD. A background (assumed to be the OD of unimplanted silica) was added to the simulated spectra.

Fig. 5
Fig. 5

Radius distributions obtained for (a) Au and (b) Cu from TEM (black curve), GISAXS (red curve), and OES (blue curve).

Equations (11)

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

α l = ln ( I inc I ) = log 1 ( e ) · log ( I inc I ) = log 1 ( e ) · OD ,
OD = log ( e ) N l σ ext = log ( e ) f V d σ ext ,
OD = log ( e ) f V d σ ext ,
σ ext = r min r max n ( r ) σ ext ( r ) d r = i = 1 N r u i n ( r i ) σ ext ( r i ) ,
V = 4 3 π r min r max n ( r ) r 3 d r = 4 3 π i = 1 N r u i n ( r i ) r i 3 ,
n ( r ) = C × exp ( ( r r n ) 2 2 σ n 2 ) ,
min [ f ( x ) ] l x u ,
χ 2 ( r n , σ n , n matrix , f ) = 1 N i = 1 N ( OD i ( λ i , r n , σ n , n matrix , f ) OD exp i ) 2 OD exp i ,
G k ε G ,
| ( χ 2 ) ( i + 1 ) ( χ 2 ) ( i ) | ε F · max { ( χ 2 ) ( i ) , ( χ 2 ) ( i + 1 ) , 1 } ,
| X k ( i + 1 ) X k ( i ) | ε X ,

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