Abstract

This paper is devoted to the study of light scattering in inhomogeneous glasses. The spectral behavior of the extinction coefficient of the initial sodium borosilicate glass and two glasses obtained by heat treatment is experimentally studied. It is established that the extinction coefficient of heat-treated glasses in the visible region is determined by the scattering of light. Experimental data on the anomalous spectral dependence of the extinction coefficient of the glass subjected to more prolonged heat treatment are compared with the results of calculations carried out in terms of various scattering models based on literature data on the structure of this glass, which consists of liquation spherical particles in a matrix. It is shown that the ordering effects observed earlier in the relative position of the particles play an important role in the light scattering. It is pointed out that, to theoretically describe the scattering properties of a system of polydisperse particles, it is necessary to know the pairwise correlation function of the particles, which depends on the size of the particles in the pair.

© 2014 Optical Society of America

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  1. N. S.  Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30, 99 (1978).
    [CrossRef]
  2. D. I.  Levin, “Rayleigh scattering in glasses and the structure of glass,” in The Structure of Glass. Papers of the Conference on the Structure of Glass (Izd. Akad. Nauk SSSR, Moscow, 1955), pp. 198–201.
  3. M. M.  Gurevich, “Spectral dependence of light scattering in sodium borosilicate glasses,” in The Structure of Glass. Papers of the Conference on the Structure of Glass (Izd. Akad. Nauk SSSR, Moscow1955), pp. 202–206.
  4. A. I.  Kolyadin, “Anomalous scattering of light in glass,” Opt. Spektrosk. 1, 907 (1956).
  5. N. A.  Voĭshvillo, “The effect of heat treatment on the scattering properties of sodium borosilicate glass,” Opt. Spektrosk. 2, 371 (1957).
  6. N. A.  Voĭshvillo, “The effect of heat treatment on the scattering indices of sodium borosilicate glass,” Opt. Spektrosk. 3, 281 (1957).
  7. K. S.  Shifrin, Light Scattering in a Turbid Medium (GITTL, Moscow, 1951).
  8. N. S.  Andreev, V. I.  Aver’yanov, N. A.  Voĭshvillo, “Structural interpretation of anomalous scattering of visible light in sodium borosilicate glasses,” Fiz. Tverd. Tela (Leningrad) 2, 1011 (1960) [Sov. Phys. Solid State 2, 916 (1960)].
  9. V. P.  Dik, A. P.  Ivanov, “Limits of applicability of the interference approximation for description of extinction of light in disperse media with high concentration of particles,” Opt. Spektrosk. 86, 1010 (1999) [Opt. Spectrosc. 86, 909 (1999)].
  10. J. K.  Percus, G. J.  Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1 (1958).
    [CrossRef]
  11. M. P.  Shepilov, “The problem of theoretically describing anomalous light scattering by liquating glasses, caused by interparticle interference,” Opt. Zh. 70, No. 12, 61 (2003) [J. Opt. Technol. 70, 882 (2003)].
  12. M. P.  Shepilov, “On the problem of theoretical description of anomalous light scattering by phase-separated glasses,” Phys. Chem. Glasses 46, 173 (2005).
  13. V.  Debye, “Über die Zerstreuung von Röntgenstrahlen an amorphen Körpern,” Phys. Zs. 28, No. 3, 135 (1927).
  14. A. E.  Kalmykov, M. P.  Shepilov, G. A.  Sycheva, “Electron-microscope study of the spatial ordering of particles formed in the process of liquation in sodium borosilicate glass,” Fiz. Khim. Stekla 26, 292 (2000).
  15. M. P.  Shepilov, A. E.  Kalmykov, “The observation of correlations in mutual spatial arrangement of phase-separated particles in glass by stereological method,” Glass Sci. Technol. 72, 458 (2002).
  16. M. P.  Shepilov, “On light scattering in fluorozirconate glass–ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30, 839 (2008).
  17. M. P.  Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31, 385 (2008).
  18. M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Liquid–liquid phase separation in sodium borosilicate glass: ordering phenomena in particle arrangement,” J. Non-Cryst. Sol. 353, 2415 (2007).
  19. M. P.  Shepilov, G. T.  Petrovskiĭ, A. E.  Kalmykov, “Electron-microscope study of ordering effects in the relative position of liquation particles in sodium borosilicate glass,” Opt. Zh. 73, No. 9, 34 (2006) [J. Opt. Technol. 73, 602 (2006)].
  20. M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Ordering effects in spatial arrangement of particles in phase-separated sodium borosilicate glass,” Phys. Chem. Glasses 47, 339 (2006).
  21. C. F.  Bohren, D. E.  Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).
  22. O. V.  Mazurin, M. V.  Strel’tsina, T. P.  Shvaĭko–Shvaĭkovskaya, Properties of Glasses and Glass-Forming Melts, vol. III, part 1 (Nauka, Leningrad, 1977).
  23. D.  Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier Pub. Co., Inc., New York, 1969).
  24. V. P.  Dik, V. A.  Loĭko, “Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles,” Opt. Spektrosk. 91, 655 (2001) [Opt. Spectrosc. 91, 618 (2001)].
  25. M. P.  Shepilov, A. E.  Kalmykov, “On taking into account the polydisperseness of particles formed in the course of phase separation in glass, with determination of their pairwise correlation function by a stereological method,” Fiz. Khim. Stekla 26, 609 (2000).
  26. M. P.  Shepilov, “Calculation of kinetics of metastable liquid–liquid phase separation for the model with simultaneous nucleation of particles,” J. Non-Cryst. Solids. 146, 1 (1992).
  27. M. P.  Shepilov, “A model for calculation of isothermal kinetics of the nucleation-and-growth type phase separation in the course of one-step heat treatment,” J. Non-Cryst. Sol. 208, 64 (1996).

2008

M. P.  Shepilov, “On light scattering in fluorozirconate glass–ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30, 839 (2008).

M. P.  Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31, 385 (2008).

2007

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Liquid–liquid phase separation in sodium borosilicate glass: ordering phenomena in particle arrangement,” J. Non-Cryst. Sol. 353, 2415 (2007).

2006

M. P.  Shepilov, G. T.  Petrovskiĭ, A. E.  Kalmykov, “Electron-microscope study of ordering effects in the relative position of liquation particles in sodium borosilicate glass,” Opt. Zh. 73, No. 9, 34 (2006) [J. Opt. Technol. 73, 602 (2006)].

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Ordering effects in spatial arrangement of particles in phase-separated sodium borosilicate glass,” Phys. Chem. Glasses 47, 339 (2006).

2005

M. P.  Shepilov, “On the problem of theoretical description of anomalous light scattering by phase-separated glasses,” Phys. Chem. Glasses 46, 173 (2005).

2003

M. P.  Shepilov, “The problem of theoretically describing anomalous light scattering by liquating glasses, caused by interparticle interference,” Opt. Zh. 70, No. 12, 61 (2003) [J. Opt. Technol. 70, 882 (2003)].

2002

M. P.  Shepilov, A. E.  Kalmykov, “The observation of correlations in mutual spatial arrangement of phase-separated particles in glass by stereological method,” Glass Sci. Technol. 72, 458 (2002).

2001

V. P.  Dik, V. A.  Loĭko, “Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles,” Opt. Spektrosk. 91, 655 (2001) [Opt. Spectrosc. 91, 618 (2001)].

2000

M. P.  Shepilov, A. E.  Kalmykov, “On taking into account the polydisperseness of particles formed in the course of phase separation in glass, with determination of their pairwise correlation function by a stereological method,” Fiz. Khim. Stekla 26, 609 (2000).

A. E.  Kalmykov, M. P.  Shepilov, G. A.  Sycheva, “Electron-microscope study of the spatial ordering of particles formed in the process of liquation in sodium borosilicate glass,” Fiz. Khim. Stekla 26, 292 (2000).

1999

V. P.  Dik, A. P.  Ivanov, “Limits of applicability of the interference approximation for description of extinction of light in disperse media with high concentration of particles,” Opt. Spektrosk. 86, 1010 (1999) [Opt. Spectrosc. 86, 909 (1999)].

1996

M. P.  Shepilov, “A model for calculation of isothermal kinetics of the nucleation-and-growth type phase separation in the course of one-step heat treatment,” J. Non-Cryst. Sol. 208, 64 (1996).

1992

M. P.  Shepilov, “Calculation of kinetics of metastable liquid–liquid phase separation for the model with simultaneous nucleation of particles,” J. Non-Cryst. Solids. 146, 1 (1992).

1978

N. S.  Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30, 99 (1978).
[CrossRef]

1960

N. S.  Andreev, V. I.  Aver’yanov, N. A.  Voĭshvillo, “Structural interpretation of anomalous scattering of visible light in sodium borosilicate glasses,” Fiz. Tverd. Tela (Leningrad) 2, 1011 (1960) [Sov. Phys. Solid State 2, 916 (1960)].

1958

J. K.  Percus, G. J.  Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1 (1958).
[CrossRef]

1957

N. A.  Voĭshvillo, “The effect of heat treatment on the scattering properties of sodium borosilicate glass,” Opt. Spektrosk. 2, 371 (1957).

N. A.  Voĭshvillo, “The effect of heat treatment on the scattering indices of sodium borosilicate glass,” Opt. Spektrosk. 3, 281 (1957).

1956

A. I.  Kolyadin, “Anomalous scattering of light in glass,” Opt. Spektrosk. 1, 907 (1956).

1927

V.  Debye, “Über die Zerstreuung von Röntgenstrahlen an amorphen Körpern,” Phys. Zs. 28, No. 3, 135 (1927).

Andreev, N. S.

N. S.  Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30, 99 (1978).
[CrossRef]

N. S.  Andreev, V. I.  Aver’yanov, N. A.  Voĭshvillo, “Structural interpretation of anomalous scattering of visible light in sodium borosilicate glasses,” Fiz. Tverd. Tela (Leningrad) 2, 1011 (1960) [Sov. Phys. Solid State 2, 916 (1960)].

Aver’yanov, V. I.

N. S.  Andreev, V. I.  Aver’yanov, N. A.  Voĭshvillo, “Structural interpretation of anomalous scattering of visible light in sodium borosilicate glasses,” Fiz. Tverd. Tela (Leningrad) 2, 1011 (1960) [Sov. Phys. Solid State 2, 916 (1960)].

Bohren, C. F.

C. F.  Bohren, D. E.  Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).

Debye, V.

V.  Debye, “Über die Zerstreuung von Röntgenstrahlen an amorphen Körpern,” Phys. Zs. 28, No. 3, 135 (1927).

Deirmendjian, D.

D.  Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier Pub. Co., Inc., New York, 1969).

Dik, V. P.

V. P.  Dik, V. A.  Loĭko, “Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles,” Opt. Spektrosk. 91, 655 (2001) [Opt. Spectrosc. 91, 618 (2001)].

V. P.  Dik, A. P.  Ivanov, “Limits of applicability of the interference approximation for description of extinction of light in disperse media with high concentration of particles,” Opt. Spektrosk. 86, 1010 (1999) [Opt. Spectrosc. 86, 909 (1999)].

Gurevich, M. M.

M. M.  Gurevich, “Spectral dependence of light scattering in sodium borosilicate glasses,” in The Structure of Glass. Papers of the Conference on the Structure of Glass (Izd. Akad. Nauk SSSR, Moscow1955), pp. 202–206.

Huffman, D. E.

C. F.  Bohren, D. E.  Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).

Ivanov, A. P.

V. P.  Dik, A. P.  Ivanov, “Limits of applicability of the interference approximation for description of extinction of light in disperse media with high concentration of particles,” Opt. Spektrosk. 86, 1010 (1999) [Opt. Spectrosc. 86, 909 (1999)].

Kalmykov, A. E.

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Liquid–liquid phase separation in sodium borosilicate glass: ordering phenomena in particle arrangement,” J. Non-Cryst. Sol. 353, 2415 (2007).

M. P.  Shepilov, G. T.  Petrovskiĭ, A. E.  Kalmykov, “Electron-microscope study of ordering effects in the relative position of liquation particles in sodium borosilicate glass,” Opt. Zh. 73, No. 9, 34 (2006) [J. Opt. Technol. 73, 602 (2006)].

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Ordering effects in spatial arrangement of particles in phase-separated sodium borosilicate glass,” Phys. Chem. Glasses 47, 339 (2006).

M. P.  Shepilov, A. E.  Kalmykov, “The observation of correlations in mutual spatial arrangement of phase-separated particles in glass by stereological method,” Glass Sci. Technol. 72, 458 (2002).

A. E.  Kalmykov, M. P.  Shepilov, G. A.  Sycheva, “Electron-microscope study of the spatial ordering of particles formed in the process of liquation in sodium borosilicate glass,” Fiz. Khim. Stekla 26, 292 (2000).

M. P.  Shepilov, A. E.  Kalmykov, “On taking into account the polydisperseness of particles formed in the course of phase separation in glass, with determination of their pairwise correlation function by a stereological method,” Fiz. Khim. Stekla 26, 609 (2000).

Kolyadin, A. I.

A. I.  Kolyadin, “Anomalous scattering of light in glass,” Opt. Spektrosk. 1, 907 (1956).

Levin, D. I.

D. I.  Levin, “Rayleigh scattering in glasses and the structure of glass,” in The Structure of Glass. Papers of the Conference on the Structure of Glass (Izd. Akad. Nauk SSSR, Moscow, 1955), pp. 198–201.

Loiko, V. A.

V. P.  Dik, V. A.  Loĭko, “Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles,” Opt. Spektrosk. 91, 655 (2001) [Opt. Spectrosc. 91, 618 (2001)].

Mazurin, O. V.

O. V.  Mazurin, M. V.  Strel’tsina, T. P.  Shvaĭko–Shvaĭkovskaya, Properties of Glasses and Glass-Forming Melts, vol. III, part 1 (Nauka, Leningrad, 1977).

Percus, J. K.

J. K.  Percus, G. J.  Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1 (1958).
[CrossRef]

Petrovskii, G. T.

M. P.  Shepilov, G. T.  Petrovskiĭ, A. E.  Kalmykov, “Electron-microscope study of ordering effects in the relative position of liquation particles in sodium borosilicate glass,” Opt. Zh. 73, No. 9, 34 (2006) [J. Opt. Technol. 73, 602 (2006)].

Shepilov, M. P.

M. P.  Shepilov, “On light scattering in fluorozirconate glass–ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30, 839 (2008).

M. P.  Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31, 385 (2008).

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Liquid–liquid phase separation in sodium borosilicate glass: ordering phenomena in particle arrangement,” J. Non-Cryst. Sol. 353, 2415 (2007).

M. P.  Shepilov, G. T.  Petrovskiĭ, A. E.  Kalmykov, “Electron-microscope study of ordering effects in the relative position of liquation particles in sodium borosilicate glass,” Opt. Zh. 73, No. 9, 34 (2006) [J. Opt. Technol. 73, 602 (2006)].

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Ordering effects in spatial arrangement of particles in phase-separated sodium borosilicate glass,” Phys. Chem. Glasses 47, 339 (2006).

M. P.  Shepilov, “On the problem of theoretical description of anomalous light scattering by phase-separated glasses,” Phys. Chem. Glasses 46, 173 (2005).

M. P.  Shepilov, “The problem of theoretically describing anomalous light scattering by liquating glasses, caused by interparticle interference,” Opt. Zh. 70, No. 12, 61 (2003) [J. Opt. Technol. 70, 882 (2003)].

M. P.  Shepilov, A. E.  Kalmykov, “The observation of correlations in mutual spatial arrangement of phase-separated particles in glass by stereological method,” Glass Sci. Technol. 72, 458 (2002).

A. E.  Kalmykov, M. P.  Shepilov, G. A.  Sycheva, “Electron-microscope study of the spatial ordering of particles formed in the process of liquation in sodium borosilicate glass,” Fiz. Khim. Stekla 26, 292 (2000).

M. P.  Shepilov, A. E.  Kalmykov, “On taking into account the polydisperseness of particles formed in the course of phase separation in glass, with determination of their pairwise correlation function by a stereological method,” Fiz. Khim. Stekla 26, 609 (2000).

M. P.  Shepilov, “A model for calculation of isothermal kinetics of the nucleation-and-growth type phase separation in the course of one-step heat treatment,” J. Non-Cryst. Sol. 208, 64 (1996).

M. P.  Shepilov, “Calculation of kinetics of metastable liquid–liquid phase separation for the model with simultaneous nucleation of particles,” J. Non-Cryst. Solids. 146, 1 (1992).

Shifrin, K. S.

K. S.  Shifrin, Light Scattering in a Turbid Medium (GITTL, Moscow, 1951).

Shvaiko–Shvaikovskaya, T. P.

O. V.  Mazurin, M. V.  Strel’tsina, T. P.  Shvaĭko–Shvaĭkovskaya, Properties of Glasses and Glass-Forming Melts, vol. III, part 1 (Nauka, Leningrad, 1977).

Strel’tsina, M. V.

O. V.  Mazurin, M. V.  Strel’tsina, T. P.  Shvaĭko–Shvaĭkovskaya, Properties of Glasses and Glass-Forming Melts, vol. III, part 1 (Nauka, Leningrad, 1977).

Sycheva, G. A.

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Liquid–liquid phase separation in sodium borosilicate glass: ordering phenomena in particle arrangement,” J. Non-Cryst. Sol. 353, 2415 (2007).

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Ordering effects in spatial arrangement of particles in phase-separated sodium borosilicate glass,” Phys. Chem. Glasses 47, 339 (2006).

A. E.  Kalmykov, M. P.  Shepilov, G. A.  Sycheva, “Electron-microscope study of the spatial ordering of particles formed in the process of liquation in sodium borosilicate glass,” Fiz. Khim. Stekla 26, 292 (2000).

Voishvillo, N. A.

N. S.  Andreev, V. I.  Aver’yanov, N. A.  Voĭshvillo, “Structural interpretation of anomalous scattering of visible light in sodium borosilicate glasses,” Fiz. Tverd. Tela (Leningrad) 2, 1011 (1960) [Sov. Phys. Solid State 2, 916 (1960)].

N. A.  Voĭshvillo, “The effect of heat treatment on the scattering properties of sodium borosilicate glass,” Opt. Spektrosk. 2, 371 (1957).

N. A.  Voĭshvillo, “The effect of heat treatment on the scattering indices of sodium borosilicate glass,” Opt. Spektrosk. 3, 281 (1957).

Yevick, G. J.

J. K.  Percus, G. J.  Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1 (1958).
[CrossRef]

Fiz. Khim. Stekla

A. E.  Kalmykov, M. P.  Shepilov, G. A.  Sycheva, “Electron-microscope study of the spatial ordering of particles formed in the process of liquation in sodium borosilicate glass,” Fiz. Khim. Stekla 26, 292 (2000).

M. P.  Shepilov, A. E.  Kalmykov, “On taking into account the polydisperseness of particles formed in the course of phase separation in glass, with determination of their pairwise correlation function by a stereological method,” Fiz. Khim. Stekla 26, 609 (2000).

Fiz. Tverd. Tela (Leningrad)

N. S.  Andreev, V. I.  Aver’yanov, N. A.  Voĭshvillo, “Structural interpretation of anomalous scattering of visible light in sodium borosilicate glasses,” Fiz. Tverd. Tela (Leningrad) 2, 1011 (1960) [Sov. Phys. Solid State 2, 916 (1960)].

Glass Sci. Technol.

M. P.  Shepilov, A. E.  Kalmykov, “The observation of correlations in mutual spatial arrangement of phase-separated particles in glass by stereological method,” Glass Sci. Technol. 72, 458 (2002).

J. Non-Cryst. Sol.

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Liquid–liquid phase separation in sodium borosilicate glass: ordering phenomena in particle arrangement,” J. Non-Cryst. Sol. 353, 2415 (2007).

M. P.  Shepilov, “A model for calculation of isothermal kinetics of the nucleation-and-growth type phase separation in the course of one-step heat treatment,” J. Non-Cryst. Sol. 208, 64 (1996).

J. Non-Cryst. Solids

N. S.  Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30, 99 (1978).
[CrossRef]

J. Non-Cryst. Solids.

M. P.  Shepilov, “Calculation of kinetics of metastable liquid–liquid phase separation for the model with simultaneous nucleation of particles,” J. Non-Cryst. Solids. 146, 1 (1992).

Opt. Mater.

M. P.  Shepilov, “On light scattering in fluorozirconate glass–ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30, 839 (2008).

M. P.  Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31, 385 (2008).

Opt. Spektrosk.

V. P.  Dik, A. P.  Ivanov, “Limits of applicability of the interference approximation for description of extinction of light in disperse media with high concentration of particles,” Opt. Spektrosk. 86, 1010 (1999) [Opt. Spectrosc. 86, 909 (1999)].

A. I.  Kolyadin, “Anomalous scattering of light in glass,” Opt. Spektrosk. 1, 907 (1956).

N. A.  Voĭshvillo, “The effect of heat treatment on the scattering properties of sodium borosilicate glass,” Opt. Spektrosk. 2, 371 (1957).

N. A.  Voĭshvillo, “The effect of heat treatment on the scattering indices of sodium borosilicate glass,” Opt. Spektrosk. 3, 281 (1957).

V. P.  Dik, V. A.  Loĭko, “Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles,” Opt. Spektrosk. 91, 655 (2001) [Opt. Spectrosc. 91, 618 (2001)].

Opt. Zh.

M. P.  Shepilov, “The problem of theoretically describing anomalous light scattering by liquating glasses, caused by interparticle interference,” Opt. Zh. 70, No. 12, 61 (2003) [J. Opt. Technol. 70, 882 (2003)].

M. P.  Shepilov, G. T.  Petrovskiĭ, A. E.  Kalmykov, “Electron-microscope study of ordering effects in the relative position of liquation particles in sodium borosilicate glass,” Opt. Zh. 73, No. 9, 34 (2006) [J. Opt. Technol. 73, 602 (2006)].

Phys. Chem. Glasses

M. P.  Shepilov, A. E.  Kalmykov, G. A.  Sycheva, “Ordering effects in spatial arrangement of particles in phase-separated sodium borosilicate glass,” Phys. Chem. Glasses 47, 339 (2006).

M. P.  Shepilov, “On the problem of theoretical description of anomalous light scattering by phase-separated glasses,” Phys. Chem. Glasses 46, 173 (2005).

Phys. Rev.

J. K.  Percus, G. J.  Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1 (1958).
[CrossRef]

Phys. Zs.

V.  Debye, “Über die Zerstreuung von Röntgenstrahlen an amorphen Körpern,” Phys. Zs. 28, No. 3, 135 (1927).

Other

D. I.  Levin, “Rayleigh scattering in glasses and the structure of glass,” in The Structure of Glass. Papers of the Conference on the Structure of Glass (Izd. Akad. Nauk SSSR, Moscow, 1955), pp. 198–201.

M. M.  Gurevich, “Spectral dependence of light scattering in sodium borosilicate glasses,” in The Structure of Glass. Papers of the Conference on the Structure of Glass (Izd. Akad. Nauk SSSR, Moscow1955), pp. 202–206.

K. S.  Shifrin, Light Scattering in a Turbid Medium (GITTL, Moscow, 1951).

C. F.  Bohren, D. E.  Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).

O. V.  Mazurin, M. V.  Strel’tsina, T. P.  Shvaĭko–Shvaĭkovskaya, Properties of Glasses and Glass-Forming Melts, vol. III, part 1 (Nauka, Leningrad, 1977).

D.  Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier Pub. Co., Inc., New York, 1969).

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