Abstract

A model that predicts the material additivity of the thermal expansion coefficient in the binary silicate glasses most commonly used for present (GeO2-SiO2, P2O5-SiO2, B2O3-SiO2, and Al2O3-SiO2) and emerging (BaO-SiO2) optical fibers is proposed. This model is based on a derivation of the expression for the coefficient of thermal expansion in isotropic solids, and gives direct insight on the parameters that govern its additivity in silicate glasses. Furthermore, a consideration of the local structural environment of the glass system is necessary to fully describe its additivity behavior in the investigated systems. This Letter is important for better characterizing and understanding of the impact of temperature and internal stresses on the behavior of optical fibers.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Ultraviolet photolytic-induced changes in optical fibers: the thermal expansion coefficient

Kin S. Chiang, Mark G. Sceats, and Danny Wong
Opt. Lett. 18(12) 965-967 (1993)

On the thermo-optic coefficient of P2O5 in SiO2

P. Dragic, M. Cavillon, and J. Ballato
Opt. Mater. Express 7(10) 3654-3661 (2017)

References

  • View by:
  • |
  • |
  • |

  1. J. Noda, K. Okamoto, and Y. Sasaki, J. Lightwave Technol. 4, 1071 (1986).
    [Crossref]
  2. P. D. Dragic, S. W. Martin, A. Ballato, and J. Ballato, Int. J. Appl. Glass Sci. 7, 3 (2016).
    [Crossref]
  3. L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).
  4. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, Opt. Express 19, 13218 (2011).
    [Crossref]
  5. L. Dong, Opt. Express 21, 915 (2013).
  6. A. Winkelmann and O. Schott, Ann. Phys. 287, 730 (1894).
    [Crossref]
  7. S. English and W. E. S. Turner, J. Am. Ceram. Soc. 10, 551 (1927).
    [Crossref]
  8. F. P. Hall, J. Am. Ceram. Soc. 13, 182 (1930).
    [Crossref]
  9. P. Gilard and L. Dubrul, Verre Silic. Ind. 5, 122 (1934).
  10. H. Doweidar, Phys. Chem. Glasses 42, 158 (2001).
  11. P. Dragic, C. Kucera, J. Furtick, J. Guerrier, T. Hawkins, and J. Ballato, Opt. Express 21, 10924 (2013).
    [Crossref]
  12. P. D. Dragic, Electron. Lett. 45, 256 (2009).
    [Crossref]
  13. F. D. Bloss, Am. Mineral. 37, 967 (1952).
  14. T. Fujii, Am. Minerol. 45, 370 (1960).
  15. E. M. Dianov and V. M. Mashinsky, J. Lightwave Technol. 23, 3500 (2005).
    [Crossref]
  16. P. D. Dragic, J. Lightwave Technol. 29, 967 (2011).
    [Crossref]
  17. P. Law, A. Croteau, and P. D. Dragic, Opt. Mater. Express 1, 686 (2011).
    [Crossref]
  18. C. M. Gilmore, Materials Science and Engineering Properties (Cengage, 2013).
  19. E. F. Riebling, J. Am. Ceram. Soc. 51, 143 (1968).
    [Crossref]
  20. Y. Y. Huang, A. Sarkar, and P. C. Schultz, J. Non-Cryst. Solids 27, 29 (1978).
    [Crossref]
  21. N. P. Bansal and R. Doremus, Handbook of Glass Properties, Methods for the Study of Marine Benthos (2013), pp. i–xvii.
  22. A. Cousen and W. E. S. Turner, J. Soc. Glass Technol. 12, 169 (1928).
  23. B. G. Varshal, E. M. Rabinovich, A. V. Levitina, and N. M. Vaisfeld, Steklovbraznye Sistemy i Novye Stekla na ikh Osnove (1971), p. 86.
  24. P. C. Schultz, “Fused P2O5 type glasses,” U.S. patent4042404 (August 16, 1977).
  25. C. L. Thompson, “Influence of the silica content upon the properties of refractories,” Ph.D. dissertation (University of Illinois, 1936).
  26. H. Doweidar, J. Non-Cryst. Solids 357, 1665 (2011).
    [Crossref]
  27. V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
    [Crossref]
  28. E. M. Birtch and J. E. Shelby, Phys. Chem. Glasses 47, 182 (2006).
  29. H. F. Shermer, J. Res. Natl. Bur. Stand. 56, 73 (1956).
    [Crossref]
  30. E. T. Y. Lee and E. R. M. Taylor, Opt. Mater. 28, 200 (2006).
    [Crossref]
  31. M. Cavillon, J. Furtick, C. J. Kucera, C. Ryan, M. Tuggle, M. Jones, T. W. Hawkins, P. Dragic, and J. Ballato, J. Lightwave Technol. 34, 1435 (2016).
    [Crossref]
  32. R. M. Waxler and C. E. Weir, J. Res. Natl. Bur. Stand.A 69A, 325 (1965).
    [Crossref]
  33. F. Pockels, Ann. Phys. 314, 220 (1902).
    [Crossref]
  34. K. Vedam, E. D. D. Schmidt, and R. Roy, J. Am. Ceram. Soc. 49, 531 (1966).
    [Crossref]
  35. B. Bendow, P. D. Gianino, Y. F. Tsay, and S. S. Mitra, Appl. Opt. 13, 2382 (1974).
    [Crossref]
  36. P. Dragic, M. Cavillon, and J. Ballato, “On the thermo-optic coefficient of P2O5 in SiO2,” Opt. Mater. Express (submitted).

2016 (2)

2013 (2)

2011 (4)

2009 (1)

P. D. Dragic, Electron. Lett. 45, 256 (2009).
[Crossref]

2006 (2)

E. T. Y. Lee and E. R. M. Taylor, Opt. Mater. 28, 200 (2006).
[Crossref]

E. M. Birtch and J. E. Shelby, Phys. Chem. Glasses 47, 182 (2006).

2005 (1)

2002 (1)

V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
[Crossref]

2001 (1)

H. Doweidar, Phys. Chem. Glasses 42, 158 (2001).

1986 (1)

J. Noda, K. Okamoto, and Y. Sasaki, J. Lightwave Technol. 4, 1071 (1986).
[Crossref]

1978 (1)

Y. Y. Huang, A. Sarkar, and P. C. Schultz, J. Non-Cryst. Solids 27, 29 (1978).
[Crossref]

1974 (1)

1968 (1)

E. F. Riebling, J. Am. Ceram. Soc. 51, 143 (1968).
[Crossref]

1966 (1)

K. Vedam, E. D. D. Schmidt, and R. Roy, J. Am. Ceram. Soc. 49, 531 (1966).
[Crossref]

1965 (1)

R. M. Waxler and C. E. Weir, J. Res. Natl. Bur. Stand.A 69A, 325 (1965).
[Crossref]

1960 (2)

T. Fujii, Am. Minerol. 45, 370 (1960).

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

1956 (1)

H. F. Shermer, J. Res. Natl. Bur. Stand. 56, 73 (1956).
[Crossref]

1952 (1)

F. D. Bloss, Am. Mineral. 37, 967 (1952).

1934 (1)

P. Gilard and L. Dubrul, Verre Silic. Ind. 5, 122 (1934).

1930 (1)

F. P. Hall, J. Am. Ceram. Soc. 13, 182 (1930).
[Crossref]

1928 (1)

A. Cousen and W. E. S. Turner, J. Soc. Glass Technol. 12, 169 (1928).

1927 (1)

S. English and W. E. S. Turner, J. Am. Ceram. Soc. 10, 551 (1927).
[Crossref]

1902 (1)

F. Pockels, Ann. Phys. 314, 220 (1902).
[Crossref]

1894 (1)

A. Winkelmann and O. Schott, Ann. Phys. 287, 730 (1894).
[Crossref]

Ballato, A.

P. D. Dragic, S. W. Martin, A. Ballato, and J. Ballato, Int. J. Appl. Glass Sci. 7, 3 (2016).
[Crossref]

Ballato, J.

P. D. Dragic, S. W. Martin, A. Ballato, and J. Ballato, Int. J. Appl. Glass Sci. 7, 3 (2016).
[Crossref]

M. Cavillon, J. Furtick, C. J. Kucera, C. Ryan, M. Tuggle, M. Jones, T. W. Hawkins, P. Dragic, and J. Ballato, J. Lightwave Technol. 34, 1435 (2016).
[Crossref]

P. Dragic, C. Kucera, J. Furtick, J. Guerrier, T. Hawkins, and J. Ballato, Opt. Express 21, 10924 (2013).
[Crossref]

P. Dragic, M. Cavillon, and J. Ballato, “On the thermo-optic coefficient of P2O5 in SiO2,” Opt. Mater. Express (submitted).

Bansal, N. P.

N. P. Bansal and R. Doremus, Handbook of Glass Properties, Methods for the Study of Marine Benthos (2013), pp. i–xvii.

Bendow, B.

Birtch, E. M.

E. M. Birtch and J. E. Shelby, Phys. Chem. Glasses 47, 182 (2006).

Bloss, F. D.

F. D. Bloss, Am. Mineral. 37, 967 (1952).

Cavillon, M.

M. Cavillon, J. Furtick, C. J. Kucera, C. Ryan, M. Tuggle, M. Jones, T. W. Hawkins, P. Dragic, and J. Ballato, J. Lightwave Technol. 34, 1435 (2016).
[Crossref]

P. Dragic, M. Cavillon, and J. Ballato, “On the thermo-optic coefficient of P2O5 in SiO2,” Opt. Mater. Express (submitted).

Cousen, A.

A. Cousen and W. E. S. Turner, J. Soc. Glass Technol. 12, 169 (1928).

Croteau, A.

Dianov, E. M.

E. M. Dianov and V. M. Mashinsky, J. Lightwave Technol. 23, 3500 (2005).
[Crossref]

V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
[Crossref]

Dong, L.

L. Dong, Opt. Express 21, 915 (2013).

Doremus, R.

N. P. Bansal and R. Doremus, Handbook of Glass Properties, Methods for the Study of Marine Benthos (2013), pp. i–xvii.

Doweidar, H.

H. Doweidar, J. Non-Cryst. Solids 357, 1665 (2011).
[Crossref]

H. Doweidar, Phys. Chem. Glasses 42, 158 (2001).

Dragic, P.

Dragic, P. D.

P. D. Dragic, S. W. Martin, A. Ballato, and J. Ballato, Int. J. Appl. Glass Sci. 7, 3 (2016).
[Crossref]

P. D. Dragic, J. Lightwave Technol. 29, 967 (2011).
[Crossref]

P. Law, A. Croteau, and P. D. Dragic, Opt. Mater. Express 1, 686 (2011).
[Crossref]

P. D. Dragic, Electron. Lett. 45, 256 (2009).
[Crossref]

Dubrul, L.

P. Gilard and L. Dubrul, Verre Silic. Ind. 5, 122 (1934).

Eidam, T.

English, S.

S. English and W. E. S. Turner, J. Am. Ceram. Soc. 10, 551 (1927).
[Crossref]

Fujii, T.

T. Fujii, Am. Minerol. 45, 370 (1960).

Furtick, J.

Gianino, P. D.

Gilard, P.

P. Gilard and L. Dubrul, Verre Silic. Ind. 5, 122 (1934).

Gilmore, C. M.

C. M. Gilmore, Materials Science and Engineering Properties (Cengage, 2013).

Guerrier, J.

Hall, F. P.

F. P. Hall, J. Am. Ceram. Soc. 13, 182 (1930).
[Crossref]

Hawkins, T.

Hawkins, T. W.

Huang, Y. Y.

Y. Y. Huang, A. Sarkar, and P. C. Schultz, J. Non-Cryst. Solids 27, 29 (1978).
[Crossref]

Jansen, F.

Jauregui, C.

Jones, M.

Koltashev, V. V.

V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
[Crossref]

Kucera, C.

Kucera, C. J.

Law, P.

Lee, E. T. Y.

E. T. Y. Lee and E. R. M. Taylor, Opt. Mater. 28, 200 (2006).
[Crossref]

Levitina, A. V.

B. G. Varshal, E. M. Rabinovich, A. V. Levitina, and N. M. Vaisfeld, Steklovbraznye Sistemy i Novye Stekla na ikh Osnove (1971), p. 86.

Limpert, J.

Martin, S. W.

P. D. Dragic, S. W. Martin, A. Ballato, and J. Ballato, Int. J. Appl. Glass Sci. 7, 3 (2016).
[Crossref]

Mashinsky, V. M.

Mitra, S. S.

Noda, J.

J. Noda, K. Okamoto, and Y. Sasaki, J. Lightwave Technol. 4, 1071 (1986).
[Crossref]

Okamoto, K.

J. Noda, K. Okamoto, and Y. Sasaki, J. Lightwave Technol. 4, 1071 (1986).
[Crossref]

Otto, H.-J.

Plotnichenko, V. G.

V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
[Crossref]

Pockels, F.

F. Pockels, Ann. Phys. 314, 220 (1902).
[Crossref]

Prod’homme, L.

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

Rabinovich, E. M.

B. G. Varshal, E. M. Rabinovich, A. V. Levitina, and N. M. Vaisfeld, Steklovbraznye Sistemy i Novye Stekla na ikh Osnove (1971), p. 86.

Riebling, E. F.

E. F. Riebling, J. Am. Ceram. Soc. 51, 143 (1968).
[Crossref]

Roy, R.

K. Vedam, E. D. D. Schmidt, and R. Roy, J. Am. Ceram. Soc. 49, 531 (1966).
[Crossref]

Ryan, C.

Sarkar, A.

Y. Y. Huang, A. Sarkar, and P. C. Schultz, J. Non-Cryst. Solids 27, 29 (1978).
[Crossref]

Sasaki, Y.

J. Noda, K. Okamoto, and Y. Sasaki, J. Lightwave Technol. 4, 1071 (1986).
[Crossref]

Schmidt, E. D. D.

K. Vedam, E. D. D. Schmidt, and R. Roy, J. Am. Ceram. Soc. 49, 531 (1966).
[Crossref]

Schmidt, O.

Schott, O.

A. Winkelmann and O. Schott, Ann. Phys. 287, 730 (1894).
[Crossref]

Schreiber, T.

Schultz, P. C.

Y. Y. Huang, A. Sarkar, and P. C. Schultz, J. Non-Cryst. Solids 27, 29 (1978).
[Crossref]

P. C. Schultz, “Fused P2O5 type glasses,” U.S. patent4042404 (August 16, 1977).

Shelby, J. E.

E. M. Birtch and J. E. Shelby, Phys. Chem. Glasses 47, 182 (2006).

Shermer, H. F.

H. F. Shermer, J. Res. Natl. Bur. Stand. 56, 73 (1956).
[Crossref]

Sokolov, V. O.

V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
[Crossref]

Stutzki, F.

Taylor, E. R. M.

E. T. Y. Lee and E. R. M. Taylor, Opt. Mater. 28, 200 (2006).
[Crossref]

Thompson, C. L.

C. L. Thompson, “Influence of the silica content upon the properties of refractories,” Ph.D. dissertation (University of Illinois, 1936).

Tsay, Y. F.

Tuggle, M.

Tünnermann, A.

Turner, W. E. S.

A. Cousen and W. E. S. Turner, J. Soc. Glass Technol. 12, 169 (1928).

S. English and W. E. S. Turner, J. Am. Ceram. Soc. 10, 551 (1927).
[Crossref]

Vaisfeld, N. M.

B. G. Varshal, E. M. Rabinovich, A. V. Levitina, and N. M. Vaisfeld, Steklovbraznye Sistemy i Novye Stekla na ikh Osnove (1971), p. 86.

Varshal, B. G.

B. G. Varshal, E. M. Rabinovich, A. V. Levitina, and N. M. Vaisfeld, Steklovbraznye Sistemy i Novye Stekla na ikh Osnove (1971), p. 86.

Vedam, K.

K. Vedam, E. D. D. Schmidt, and R. Roy, J. Am. Ceram. Soc. 49, 531 (1966).
[Crossref]

Waxler, R. M.

R. M. Waxler and C. E. Weir, J. Res. Natl. Bur. Stand.A 69A, 325 (1965).
[Crossref]

Weir, C. E.

R. M. Waxler and C. E. Weir, J. Res. Natl. Bur. Stand.A 69A, 325 (1965).
[Crossref]

Winkelmann, A.

A. Winkelmann and O. Schott, Ann. Phys. 287, 730 (1894).
[Crossref]

Wirth, C.

Am. Mineral. (1)

F. D. Bloss, Am. Mineral. 37, 967 (1952).

Am. Minerol. (1)

T. Fujii, Am. Minerol. 45, 370 (1960).

Ann. Phys. (2)

F. Pockels, Ann. Phys. 314, 220 (1902).
[Crossref]

A. Winkelmann and O. Schott, Ann. Phys. 287, 730 (1894).
[Crossref]

Appl. Opt. (1)

Electron. Lett. (1)

P. D. Dragic, Electron. Lett. 45, 256 (2009).
[Crossref]

Int. J. Appl. Glass Sci. (1)

P. D. Dragic, S. W. Martin, A. Ballato, and J. Ballato, Int. J. Appl. Glass Sci. 7, 3 (2016).
[Crossref]

J. Am. Ceram. Soc. (4)

S. English and W. E. S. Turner, J. Am. Ceram. Soc. 10, 551 (1927).
[Crossref]

F. P. Hall, J. Am. Ceram. Soc. 13, 182 (1930).
[Crossref]

E. F. Riebling, J. Am. Ceram. Soc. 51, 143 (1968).
[Crossref]

K. Vedam, E. D. D. Schmidt, and R. Roy, J. Am. Ceram. Soc. 49, 531 (1966).
[Crossref]

J. Lightwave Technol. (4)

J. Non-Cryst. Solids (3)

Y. Y. Huang, A. Sarkar, and P. C. Schultz, J. Non-Cryst. Solids 27, 29 (1978).
[Crossref]

H. Doweidar, J. Non-Cryst. Solids 357, 1665 (2011).
[Crossref]

V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, and E. M. Dianov, J. Non-Cryst. Solids 306, 209 (2002).
[Crossref]

J. Res. Natl. Bur. Stand. (1)

H. F. Shermer, J. Res. Natl. Bur. Stand. 56, 73 (1956).
[Crossref]

J. Res. Natl. Bur. Stand.A (1)

R. M. Waxler and C. E. Weir, J. Res. Natl. Bur. Stand.A 69A, 325 (1965).
[Crossref]

J. Soc. Glass Technol. (1)

A. Cousen and W. E. S. Turner, J. Soc. Glass Technol. 12, 169 (1928).

Opt. Express (3)

Opt. Mater. (1)

E. T. Y. Lee and E. R. M. Taylor, Opt. Mater. 28, 200 (2006).
[Crossref]

Opt. Mater. Express (1)

Phys. Chem. Glasses (3)

E. M. Birtch and J. E. Shelby, Phys. Chem. Glasses 47, 182 (2006).

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

H. Doweidar, Phys. Chem. Glasses 42, 158 (2001).

Verre Silic. Ind. (1)

P. Gilard and L. Dubrul, Verre Silic. Ind. 5, 122 (1934).

Other (6)

C. M. Gilmore, Materials Science and Engineering Properties (Cengage, 2013).

N. P. Bansal and R. Doremus, Handbook of Glass Properties, Methods for the Study of Marine Benthos (2013), pp. i–xvii.

B. G. Varshal, E. M. Rabinovich, A. V. Levitina, and N. M. Vaisfeld, Steklovbraznye Sistemy i Novye Stekla na ikh Osnove (1971), p. 86.

P. C. Schultz, “Fused P2O5 type glasses,” U.S. patent4042404 (August 16, 1977).

C. L. Thompson, “Influence of the silica content upon the properties of refractories,” Ph.D. dissertation (University of Illinois, 1936).

P. Dragic, M. Cavillon, and J. Ballato, “On the thermo-optic coefficient of P2O5 in SiO2,” Opt. Mater. Express (submitted).

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 (2)

Fig. 1.
Fig. 1.

Linear coefficient of thermal expansion ( α ) for some typical binary silicate systems as a function of non-silica content. The fitting of these data is performed with Eq. (6). Data where found in [19,20] for GeO 2 - SiO 2 , in [21] for B 2 O 3 - SiO 2 and BaO - SiO 2 , citing [22] and [23], respectively, [24] for P 2 O 5 - SiO 2 , and [25] for Al 2 O 3 - SiO 2 . All the systems together are valid within a common range of 25°C–100°C.

Fig. 2.
Fig. 2.

Modified additivity prediction of the coefficient of thermal expansion ( α ) in binary silicate glasses using Eq. (7), instead of Eq. (6), and considering the additivity of α to be a function of the variation of density per structural glass unit.

Tables (2)

Tables Icon

Table 1. Molar Mass (M) and Density ( ρ ) Used for the Calculations

Tables Icon

Table 2. Estimated Coefficient of Thermal Expansion of Amorphous Materials, Based on Additivity of Eqs. (6) and (7)

Equations (9)

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

ρ = m V .
ρ = i m i V i = i ρ i V i V i = i ρ i x i ,
x A = [ A ] M A ρ A [ A ] M A ρ A + [ B ] M B ρ B .
ρ T = i ρ i x i T .
β = 1 ρ ρ T ,
α = i α i ρ i x i ρ .
α = i α i ρ i y i ρ ,
y A = [ A ] M A ρ A T A [ A ] M A ρ A T A + [ B ] M B ρ B T B .
n = n 0 + d n d T ( T T 0 ) + n 0 3 2 ( α core α cladd in g ) × [ 2 ( p 12 υ ( p 11 + p 12 ) ) + ( p 11 2 υ p 12 ) ] ( T T 0 ) ,

Metrics