Abstract

Reflectances of two low-expansion materials, a recrystallized glass ceramic and a high silica glass, have been measured at five angles of incidence from 15° to 85° in the wavelength region from 80 to 310 Å and in some cases up to 1050 Å. Optical constants are derived and silicon core-level transitions analyzed.

© 1980 Optical Society of America

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References

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  1. The two low-expansion glasses, procured for this study by NASA, are Cer-Vit® C101 (glass A): Owens-Illinois Glass Co., Toledo, Ohio 43604, and Code 7971-ULE®-Glass (glass B): Corning Glass Works, Corning, New York 14830. The investigation of these materials does not constitute a recommendation or an endorsement by the National Bureau of Standards.
  2. O. A. Ershov, I. A. Brytov, and A. P. Lukirskii, “Reflection of x-rays from certain substances in the region from 7 to 44 Å, Opt. Spectrosc. 22, 66–69 (1967);E. P. Savinov, I. L. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, “Graphical solution of the Fresnel equations and the calculation of the optical constants in the ultrasoft x-ray region of the spectrum,” Opt. Spectrosc. 27, 179–181 (1969).
  3. J. Osantowski, “Reflectance and optical constants for Cer-Vit from 250 to 1050 Å,” J. Opt. Soc. Am. 64, 834–838 (1974).
    [CrossRef]
  4. J. Rife and J. Osantowski, “Mirror reflectivities from 50 to 150 eV,” J. Nucl. Inst. Meth. 172, 297–301 (1980).
    [CrossRef]
  5. D. L. Ederer and S. Ebner, “A User’s Guide to SURF,” Natl. Bur. Stand. Internal Report, 1976 (unpublished).
  6. Workshop on X-Ray Instrumentation for Synchrotron Radiation Research, edited by H. Winick and G. Brown, SSRL Report No. 78/04 (Stanford Synchrotron Laboratory, Stanford, 1978).
  7. A. Franks and M. Stedman, “X-ray gratings—substrate and performance studies,” J. Nucl. Instrum. Meth. 172, 249–257 (1980).
    [CrossRef]
  8. M. Born and E. Wolf, Principles of OpticsOxford, 1964).
  9. C. A. Neugebauer, “Structural disorder phenomena in thin metal films,” Phys. Thin Films 2, 1–59 (1964).
  10. V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
    [CrossRef]
  11. H. E. Bennett and J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961).
    [CrossRef]
  12. D. L. Griscom, “Electronic structure of SiO2,” J. Non-Cryst. Solids 24, 155–234 (1977).
    [CrossRef]
  13. The Physics of SiO2 and its Interfaces, edited by S. T. Pantelides (PergamonNew York, 1978).
  14. J. W. Berthold and S. F. Jacobs, “Ultraprecise thermal expansion measurements of seven low expansion materials,” Appl. Opt. 15, 2344–2347 (1976).
    [CrossRef]
  15. Chi-Tang Li and Donald R. Peacor, “The crystal structure of Li-AlSi2O6–II (“β-spodumene”),” Zeit Kris. 126, 46–65 (1968).
    [CrossRef]
  16. H. T. Smyth, “The role of transverse oxygen vibrations in thermal expansion behavior of glasses and crystals,” in Thermal Expansion edited by M. B. Graham and H. E. Hagy (AIP, New York, 1972) pp. 244–256.
  17. H. R. Phillip, “Optical transitions in crystalline and fused quartz,” Solid State Commun. 4, 73–75 (1966).
    [CrossRef]
  18. Yasuo Iguchi, “Soft x-ray spectra of solids containing silicon in tetrahedral and octahedral coordination with oxygen,” Sci. Light 26, 161–181 (1977).
  19. C. Sénémand and M. T. Costa Limo, “K x-ray spectra of amorphous and crystalline SiO2,” in Ref. 13, pp. 75–79.
  20. T. H. D. Stefano and D. E. Eastman, “Photoemission measurements of the valence levels of amorphous SiO2,” Phys. Rev. Lett. 27, 1560–1562 (1972).
    [CrossRef]
  21. W. Gudat and C. Kunz, “Yields spectroscopy and EDC spectra of LiF,” in Vacuum Ultraviolet Radiation Physics—IV, edited by E. E. Koch, R. Haensel, and C. Kunz (Pergamon, Germany, 1974) pp. 392–395.
  22. L. G. Parratt, “Surface studies of solids by total reflection of x rays,” Phys. Rev. 95, 359–369 (1954).
    [CrossRef]
  23. O. A. Ershov and A. P. Lukirskii, “Investigation of the energy structure of Si and SiO2 by ultrasoft x-ray emission and absorption spectroscopy,” Sov. Phys. Sol State 8, 1699–1703 (1967).
  24. F. Brown, R. Z. Bachrach, and M. Skibowski, “L2,3 threshold spectra of doped silicon and silcon compounds,” Phys. Rev. B 15, 4781–4788 (77).
  25. F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
    [CrossRef]
  26. C. Kunz, “Soft x-ray excitation of core electrons in metals and alloys,” in Optical Properties of Solids—New Developments, edited by B. O. Seraphin (North-Holland, Amsterdam, 1976) pp. 473–553.
  27. J. A. Tossell, “The electronic structures of silicon, aluminum, and magnesium in tetrahedral coordination with oxygen from ScF-xα M O calculations,” J. Am. Chem. Soc. 97, 4840–4844 (1975).
    [CrossRef]
  28. K. Codling and R. P. Madden, “Structure in the LII,III absorption of aluminum and its oxides,” Phys. Rev. 167, 587–591 (1968).
    [CrossRef]
  29. H. J. Hageman, W. Gudat, and C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.” Deutsches Elektronen-Synchrotron (DESY) report SR-74/7, Hamburg, Germany (unpublished).

1980 (3)

J. Rife and J. Osantowski, “Mirror reflectivities from 50 to 150 eV,” J. Nucl. Inst. Meth. 172, 297–301 (1980).
[CrossRef]

A. Franks and M. Stedman, “X-ray gratings—substrate and performance studies,” J. Nucl. Instrum. Meth. 172, 249–257 (1980).
[CrossRef]

V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
[CrossRef]

1979 (1)

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

1977 (2)

Yasuo Iguchi, “Soft x-ray spectra of solids containing silicon in tetrahedral and octahedral coordination with oxygen,” Sci. Light 26, 161–181 (1977).

D. L. Griscom, “Electronic structure of SiO2,” J. Non-Cryst. Solids 24, 155–234 (1977).
[CrossRef]

1976 (1)

1975 (1)

J. A. Tossell, “The electronic structures of silicon, aluminum, and magnesium in tetrahedral coordination with oxygen from ScF-xα M O calculations,” J. Am. Chem. Soc. 97, 4840–4844 (1975).
[CrossRef]

1974 (1)

1972 (1)

T. H. D. Stefano and D. E. Eastman, “Photoemission measurements of the valence levels of amorphous SiO2,” Phys. Rev. Lett. 27, 1560–1562 (1972).
[CrossRef]

1968 (2)

K. Codling and R. P. Madden, “Structure in the LII,III absorption of aluminum and its oxides,” Phys. Rev. 167, 587–591 (1968).
[CrossRef]

Chi-Tang Li and Donald R. Peacor, “The crystal structure of Li-AlSi2O6–II (“β-spodumene”),” Zeit Kris. 126, 46–65 (1968).
[CrossRef]

1967 (2)

O. A. Ershov, I. A. Brytov, and A. P. Lukirskii, “Reflection of x-rays from certain substances in the region from 7 to 44 Å, Opt. Spectrosc. 22, 66–69 (1967);E. P. Savinov, I. L. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, “Graphical solution of the Fresnel equations and the calculation of the optical constants in the ultrasoft x-ray region of the spectrum,” Opt. Spectrosc. 27, 179–181 (1969).

O. A. Ershov and A. P. Lukirskii, “Investigation of the energy structure of Si and SiO2 by ultrasoft x-ray emission and absorption spectroscopy,” Sov. Phys. Sol State 8, 1699–1703 (1967).

1966 (1)

H. R. Phillip, “Optical transitions in crystalline and fused quartz,” Solid State Commun. 4, 73–75 (1966).
[CrossRef]

1964 (1)

C. A. Neugebauer, “Structural disorder phenomena in thin metal films,” Phys. Thin Films 2, 1–59 (1964).

1961 (1)

1954 (1)

L. G. Parratt, “Surface studies of solids by total reflection of x rays,” Phys. Rev. 95, 359–369 (1954).
[CrossRef]

Bachrach, R. Z.

F. Brown, R. Z. Bachrach, and M. Skibowski, “L2,3 threshold spectra of doped silicon and silcon compounds,” Phys. Rev. B 15, 4781–4788 (77).

Bennett, H. E.

Bennett, J. M.

V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
[CrossRef]

Berthold, J. W.

Born, M.

M. Born and E. Wolf, Principles of OpticsOxford, 1964).

Brown, F.

F. Brown, R. Z. Bachrach, and M. Skibowski, “L2,3 threshold spectra of doped silicon and silcon compounds,” Phys. Rev. B 15, 4781–4788 (77).

Brytov, I. A.

O. A. Ershov, I. A. Brytov, and A. P. Lukirskii, “Reflection of x-rays from certain substances in the region from 7 to 44 Å, Opt. Spectrosc. 22, 66–69 (1967);E. P. Savinov, I. L. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, “Graphical solution of the Fresnel equations and the calculation of the optical constants in the ultrasoft x-ray region of the spectrum,” Opt. Spectrosc. 27, 179–181 (1969).

Codling, K.

K. Codling and R. P. Madden, “Structure in the LII,III absorption of aluminum and its oxides,” Phys. Rev. 167, 587–591 (1968).
[CrossRef]

Costa Limo, M. T.

C. Sénémand and M. T. Costa Limo, “K x-ray spectra of amorphous and crystalline SiO2,” in Ref. 13, pp. 75–79.

Eastman, D. E.

T. H. D. Stefano and D. E. Eastman, “Photoemission measurements of the valence levels of amorphous SiO2,” Phys. Rev. Lett. 27, 1560–1562 (1972).
[CrossRef]

Ebner, S.

D. L. Ederer and S. Ebner, “A User’s Guide to SURF,” Natl. Bur. Stand. Internal Report, 1976 (unpublished).

Ederer, D. L.

D. L. Ederer and S. Ebner, “A User’s Guide to SURF,” Natl. Bur. Stand. Internal Report, 1976 (unpublished).

Elson, J. M.

V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
[CrossRef]

Ershov, O. A.

O. A. Ershov, I. A. Brytov, and A. P. Lukirskii, “Reflection of x-rays from certain substances in the region from 7 to 44 Å, Opt. Spectrosc. 22, 66–69 (1967);E. P. Savinov, I. L. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, “Graphical solution of the Fresnel equations and the calculation of the optical constants in the ultrasoft x-ray region of the spectrum,” Opt. Spectrosc. 27, 179–181 (1969).

O. A. Ershov and A. P. Lukirskii, “Investigation of the energy structure of Si and SiO2 by ultrasoft x-ray emission and absorption spectroscopy,” Sov. Phys. Sol State 8, 1699–1703 (1967).

Franks, A.

A. Franks and M. Stedman, “X-ray gratings—substrate and performance studies,” J. Nucl. Instrum. Meth. 172, 249–257 (1980).
[CrossRef]

Griscom, D. L.

D. L. Griscom, “Electronic structure of SiO2,” J. Non-Cryst. Solids 24, 155–234 (1977).
[CrossRef]

Grunthaner, F. J.

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

Grunthaner, P. J.

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

Gudat, W.

H. J. Hageman, W. Gudat, and C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.” Deutsches Elektronen-Synchrotron (DESY) report SR-74/7, Hamburg, Germany (unpublished).

W. Gudat and C. Kunz, “Yields spectroscopy and EDC spectra of LiF,” in Vacuum Ultraviolet Radiation Physics—IV, edited by E. E. Koch, R. Haensel, and C. Kunz (Pergamon, Germany, 1974) pp. 392–395.

Hageman, H. J.

H. J. Hageman, W. Gudat, and C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.” Deutsches Elektronen-Synchrotron (DESY) report SR-74/7, Hamburg, Germany (unpublished).

Iguchi, Yasuo

Yasuo Iguchi, “Soft x-ray spectra of solids containing silicon in tetrahedral and octahedral coordination with oxygen,” Sci. Light 26, 161–181 (1977).

Jacobs, S. F.

Jones, V. O.

V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
[CrossRef]

Kunz, C.

W. Gudat and C. Kunz, “Yields spectroscopy and EDC spectra of LiF,” in Vacuum Ultraviolet Radiation Physics—IV, edited by E. E. Koch, R. Haensel, and C. Kunz (Pergamon, Germany, 1974) pp. 392–395.

H. J. Hageman, W. Gudat, and C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.” Deutsches Elektronen-Synchrotron (DESY) report SR-74/7, Hamburg, Germany (unpublished).

C. Kunz, “Soft x-ray excitation of core electrons in metals and alloys,” in Optical Properties of Solids—New Developments, edited by B. O. Seraphin (North-Holland, Amsterdam, 1976) pp. 473–553.

Lewis, B. F.

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

Li, Chi-Tang

Chi-Tang Li and Donald R. Peacor, “The crystal structure of Li-AlSi2O6–II (“β-spodumene”),” Zeit Kris. 126, 46–65 (1968).
[CrossRef]

Lukirskii, A. P.

O. A. Ershov and A. P. Lukirskii, “Investigation of the energy structure of Si and SiO2 by ultrasoft x-ray emission and absorption spectroscopy,” Sov. Phys. Sol State 8, 1699–1703 (1967).

O. A. Ershov, I. A. Brytov, and A. P. Lukirskii, “Reflection of x-rays from certain substances in the region from 7 to 44 Å, Opt. Spectrosc. 22, 66–69 (1967);E. P. Savinov, I. L. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, “Graphical solution of the Fresnel equations and the calculation of the optical constants in the ultrasoft x-ray region of the spectrum,” Opt. Spectrosc. 27, 179–181 (1969).

Madden, R. P.

K. Codling and R. P. Madden, “Structure in the LII,III absorption of aluminum and its oxides,” Phys. Rev. 167, 587–591 (1968).
[CrossRef]

Madhukar, A.

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

Maserjian, J.

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

Neugebauer, C. A.

C. A. Neugebauer, “Structural disorder phenomena in thin metal films,” Phys. Thin Films 2, 1–59 (1964).

Osantowski, J.

J. Rife and J. Osantowski, “Mirror reflectivities from 50 to 150 eV,” J. Nucl. Inst. Meth. 172, 297–301 (1980).
[CrossRef]

J. Osantowski, “Reflectance and optical constants for Cer-Vit from 250 to 1050 Å,” J. Opt. Soc. Am. 64, 834–838 (1974).
[CrossRef]

Pantelides, S. T.

The Physics of SiO2 and its Interfaces, edited by S. T. Pantelides (PergamonNew York, 1978).

Parratt, L. G.

L. G. Parratt, “Surface studies of solids by total reflection of x rays,” Phys. Rev. 95, 359–369 (1954).
[CrossRef]

Peacor, Donald R.

Chi-Tang Li and Donald R. Peacor, “The crystal structure of Li-AlSi2O6–II (“β-spodumene”),” Zeit Kris. 126, 46–65 (1968).
[CrossRef]

Phillip, H. R.

H. R. Phillip, “Optical transitions in crystalline and fused quartz,” Solid State Commun. 4, 73–75 (1966).
[CrossRef]

Porteus, J. O.

Rehn, V.

V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
[CrossRef]

Rife, J.

J. Rife and J. Osantowski, “Mirror reflectivities from 50 to 150 eV,” J. Nucl. Inst. Meth. 172, 297–301 (1980).
[CrossRef]

Sénémand, C.

C. Sénémand and M. T. Costa Limo, “K x-ray spectra of amorphous and crystalline SiO2,” in Ref. 13, pp. 75–79.

Seraphin, B. O.

C. Kunz, “Soft x-ray excitation of core electrons in metals and alloys,” in Optical Properties of Solids—New Developments, edited by B. O. Seraphin (North-Holland, Amsterdam, 1976) pp. 473–553.

Skibowski, M.

F. Brown, R. Z. Bachrach, and M. Skibowski, “L2,3 threshold spectra of doped silicon and silcon compounds,” Phys. Rev. B 15, 4781–4788 (77).

Smyth, H. T.

H. T. Smyth, “The role of transverse oxygen vibrations in thermal expansion behavior of glasses and crystals,” in Thermal Expansion edited by M. B. Graham and H. E. Hagy (AIP, New York, 1972) pp. 244–256.

Stedman, M.

A. Franks and M. Stedman, “X-ray gratings—substrate and performance studies,” J. Nucl. Instrum. Meth. 172, 249–257 (1980).
[CrossRef]

Stefano, T. H. D.

T. H. D. Stefano and D. E. Eastman, “Photoemission measurements of the valence levels of amorphous SiO2,” Phys. Rev. Lett. 27, 1560–1562 (1972).
[CrossRef]

Tossell, J. A.

J. A. Tossell, “The electronic structures of silicon, aluminum, and magnesium in tetrahedral coordination with oxygen from ScF-xα M O calculations,” J. Am. Chem. Soc. 97, 4840–4844 (1975).
[CrossRef]

Vasquez, R. P.

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of OpticsOxford, 1964).

Appl. Opt. (1)

J. Am. Chem. Soc. (1)

J. A. Tossell, “The electronic structures of silicon, aluminum, and magnesium in tetrahedral coordination with oxygen from ScF-xα M O calculations,” J. Am. Chem. Soc. 97, 4840–4844 (1975).
[CrossRef]

J. Non-Cryst. Solids (1)

D. L. Griscom, “Electronic structure of SiO2,” J. Non-Cryst. Solids 24, 155–234 (1977).
[CrossRef]

J. Nucl. Inst. Meth. (1)

J. Rife and J. Osantowski, “Mirror reflectivities from 50 to 150 eV,” J. Nucl. Inst. Meth. 172, 297–301 (1980).
[CrossRef]

J. Nucl. Instrum. Meth. (2)

A. Franks and M. Stedman, “X-ray gratings—substrate and performance studies,” J. Nucl. Instrum. Meth. 172, 249–257 (1980).
[CrossRef]

V. Rehn, V. O. Jones, J. M. Elson, and J. M. Bennett, “The role of surface topography in predicting scattering at grazing incidence from optical surfaces,” J. Nucl. Instrum. Meth. 172, 307–314 (1980).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Spectrosc. (1)

O. A. Ershov, I. A. Brytov, and A. P. Lukirskii, “Reflection of x-rays from certain substances in the region from 7 to 44 Å, Opt. Spectrosc. 22, 66–69 (1967);E. P. Savinov, I. L. Lyakhovskaya, O. A. Ershov, and E. A. Kovalyeva, “Graphical solution of the Fresnel equations and the calculation of the optical constants in the ultrasoft x-ray region of the spectrum,” Opt. Spectrosc. 27, 179–181 (1969).

Phys. Rev. (2)

K. Codling and R. P. Madden, “Structure in the LII,III absorption of aluminum and its oxides,” Phys. Rev. 167, 587–591 (1968).
[CrossRef]

L. G. Parratt, “Surface studies of solids by total reflection of x rays,” Phys. Rev. 95, 359–369 (1954).
[CrossRef]

Phys. Rev. B (1)

F. Brown, R. Z. Bachrach, and M. Skibowski, “L2,3 threshold spectra of doped silicon and silcon compounds,” Phys. Rev. B 15, 4781–4788 (77).

Phys. Rev. Lett. (2)

F. J. Grunthaner, P. J. Grunthaner, R. P. Vasquez, B. F. Lewis, J. Maserjian, and A. Madhukar, “High-resolution x-ray photoelectron spectroscopy as a probe of local atomic structure: application to amorphous SiO2 and the Si-SiO2 interface,” Phys. Rev. Lett. 43, 1683–1686 (1979).
[CrossRef]

T. H. D. Stefano and D. E. Eastman, “Photoemission measurements of the valence levels of amorphous SiO2,” Phys. Rev. Lett. 27, 1560–1562 (1972).
[CrossRef]

Phys. Thin Films (1)

C. A. Neugebauer, “Structural disorder phenomena in thin metal films,” Phys. Thin Films 2, 1–59 (1964).

Sci. Light (1)

Yasuo Iguchi, “Soft x-ray spectra of solids containing silicon in tetrahedral and octahedral coordination with oxygen,” Sci. Light 26, 161–181 (1977).

Solid State Commun. (1)

H. R. Phillip, “Optical transitions in crystalline and fused quartz,” Solid State Commun. 4, 73–75 (1966).
[CrossRef]

Sov. Phys. Sol State (1)

O. A. Ershov and A. P. Lukirskii, “Investigation of the energy structure of Si and SiO2 by ultrasoft x-ray emission and absorption spectroscopy,” Sov. Phys. Sol State 8, 1699–1703 (1967).

Zeit Kris. (1)

Chi-Tang Li and Donald R. Peacor, “The crystal structure of Li-AlSi2O6–II (“β-spodumene”),” Zeit Kris. 126, 46–65 (1968).
[CrossRef]

Other (10)

H. T. Smyth, “The role of transverse oxygen vibrations in thermal expansion behavior of glasses and crystals,” in Thermal Expansion edited by M. B. Graham and H. E. Hagy (AIP, New York, 1972) pp. 244–256.

C. Sénémand and M. T. Costa Limo, “K x-ray spectra of amorphous and crystalline SiO2,” in Ref. 13, pp. 75–79.

The Physics of SiO2 and its Interfaces, edited by S. T. Pantelides (PergamonNew York, 1978).

M. Born and E. Wolf, Principles of OpticsOxford, 1964).

The two low-expansion glasses, procured for this study by NASA, are Cer-Vit® C101 (glass A): Owens-Illinois Glass Co., Toledo, Ohio 43604, and Code 7971-ULE®-Glass (glass B): Corning Glass Works, Corning, New York 14830. The investigation of these materials does not constitute a recommendation or an endorsement by the National Bureau of Standards.

D. L. Ederer and S. Ebner, “A User’s Guide to SURF,” Natl. Bur. Stand. Internal Report, 1976 (unpublished).

Workshop on X-Ray Instrumentation for Synchrotron Radiation Research, edited by H. Winick and G. Brown, SSRL Report No. 78/04 (Stanford Synchrotron Laboratory, Stanford, 1978).

W. Gudat and C. Kunz, “Yields spectroscopy and EDC spectra of LiF,” in Vacuum Ultraviolet Radiation Physics—IV, edited by E. E. Koch, R. Haensel, and C. Kunz (Pergamon, Germany, 1974) pp. 392–395.

C. Kunz, “Soft x-ray excitation of core electrons in metals and alloys,” in Optical Properties of Solids—New Developments, edited by B. O. Seraphin (North-Holland, Amsterdam, 1976) pp. 473–553.

H. J. Hageman, W. Gudat, and C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.” Deutsches Elektronen-Synchrotron (DESY) report SR-74/7, Hamburg, Germany (unpublished).

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Figures (5)

FIG 1
FIG 1

Unpolarized reflectance of glass A at 85, 80, 70, 45, and 15° angle of incidence. Note the different wavelength scales for the NASA and NBS data.

FIG. 2
FIG. 2

Unpolarized reflectance of glass B at 85, 80, 70, 45, and 15° angle of incidence. Note the different wavelength scales for the NASA and NBS data.

FIG. 3
FIG. 3

Optical constants n and k for glass A near the Si LII,III edge.

FIG. 4
FIG. 4

Optical constants n and k for glass B near the Si LII,III edge.

FIG. 5
FIG. 5

Optical constants n and k for glass A near the AlII,III edge. The edge appears at a wavelength characteristic of Al2O3 absorption.

Tables (3)

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TABLE I Optical constants for glass A1 derived from the reflectance verses angle-of-incidence method. The n and k error estimate indicates the range of reasonable intersection of the isoreflector curves in n and k space.

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TABLE II Optical constants for glass B1 derived from the reflectance versus angle-of-incidence method. The n and k error estimate indicates the range of reasonable intersection of the isoreflector curves in n and k space.

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TABLE III Sample reflectances for glass A1. The first row shows the measured reflectances, the second row the reflectance values calculated from the corresponding optical constants.

Equations (2)

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λ / [ 2 π n ( sin 2 σ / n 2 ) 1 ]
R R 0 exp [ ( 4 π δ cos σ ) 2 / λ 2 ] for λ δ .