Abstract

All-optical communication systems are the subject of intense research related to the integration of nonlinear optical materials. In sodiocalcic borophosphate glasses that contain niobium oxide and exhibit high nonlinear optical indices, planar waveguides have been formed by a Ag+–Na+ ion-exchange technique. WKB analysis has been used to characterize the diffusion profiles of silver ions exchanged in glass substrate samples chemically by an electron microprobe technique and optically by an M-line technique. These methods permit the Ag+ penetration depth and diffusion profile shape and index profiles to be determined. The results are analyzed and discussed in relation to Ca2+ concentration and exchange conditions in glasses. The Ag+ diffusion in these glasses can be almost entirely controlled for index-profile engineering.

© 2000 Optical Society of America

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References

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  1. E. M. Vogel, M. J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32, 231–253 (1991).
  2. T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).
  3. E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
    [CrossRef]
  4. T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).
  5. R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
    [CrossRef]
  6. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 408–412.
  7. R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
    [CrossRef] [PubMed]
  8. K. S. Chiang, “Construction of refractive index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
    [CrossRef]
  9. M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
    [CrossRef]
  10. J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
    [CrossRef]
  11. R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
    [CrossRef]
  12. P. J. R. Laybourn, G. Steward, “Fabrication of ion exchanged optical waveguides from dilute silver nitrate melts,” J. Quantum Electron. QE-14, 930–934 (1978).
  13. J. L. Jackel, E. M. Vogel, J. S. Aitchinson, “Ion exchanged optical waveguides for all-optical switching,” Appl. Opt. 29, 3126–3129 (1990).
    [CrossRef] [PubMed]
  14. A. A. Ahmed, E. W. Abdallah, “Effect of ion exchange and heat treatment conditions on the diffusion of silver into a soda-lime-silica glass,” Phys. Chem. Glasses 38, 42–50 (1997).

1998 (1)

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

1997 (1)

A. A. Ahmed, E. W. Abdallah, “Effect of ion exchange and heat treatment conditions on the diffusion of silver into a soda-lime-silica glass,” Phys. Chem. Glasses 38, 42–50 (1997).

1996 (1)

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

1994 (2)

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
[CrossRef]

1992 (1)

M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
[CrossRef]

1991 (1)

E. M. Vogel, M. J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32, 231–253 (1991).

1990 (1)

1988 (1)

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

1985 (1)

K. S. Chiang, “Construction of refractive index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

1978 (1)

P. J. R. Laybourn, G. Steward, “Fabrication of ion exchanged optical waveguides from dilute silver nitrate melts,” J. Quantum Electron. QE-14, 930–934 (1978).

1973 (1)

1964 (1)

R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
[CrossRef]

Abdallah, E. W.

A. A. Ahmed, E. W. Abdallah, “Effect of ion exchange and heat treatment conditions on the diffusion of silver into a soda-lime-silica glass,” Phys. Chem. Glasses 38, 42–50 (1997).

Adamietz, F.

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Ahmed, A. A.

A. A. Ahmed, E. W. Abdallah, “Effect of ion exchange and heat treatment conditions on the diffusion of silver into a soda-lime-silica glass,” Phys. Chem. Glasses 38, 42–50 (1997).

Aitchinson, J. S.

Berthereau, A.

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

Brauer, A.

M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
[CrossRef]

Canioni, L.

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Cardinal, T.

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Chiang, K. S.

K. S. Chiang, “Construction of refractive index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

Couzi, M.

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

Doremus, R. H.

R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
[CrossRef]

Ducasse, A.

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Ducel, J. F.

J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
[CrossRef]

Fargin, E.

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 408–412.

Guntau, M.

M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
[CrossRef]

Jackel, J. L.

Karthe, W.

M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
[CrossRef]

Krol, D. M.

E. M. Vogel, M. J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32, 231–253 (1991).

Laybourn, P. J. R.

P. J. R. Laybourn, G. Steward, “Fabrication of ion exchanged optical waveguides from dilute silver nitrate melts,” J. Quantum Electron. QE-14, 930–934 (1978).

Le Flem, G.

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Possner, T.

M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 408–412.

Ramaswamy, R. V.

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

Sarger, L.

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Segonds, P.

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

Sénégas, J.

J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
[CrossRef]

Srivastava, R.

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

Steward, G.

P. J. R. Laybourn, G. Steward, “Fabrication of ion exchanged optical waveguides from dilute silver nitrate melts,” J. Quantum Electron. QE-14, 930–934 (1978).

Suh, K. S.

J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 408–412.

Torge, R.

Ulrich, R.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 408–412.

Videau, J. J.

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
[CrossRef]

Villesuzanne, A.

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

Vogel, E. M.

E. M. Vogel, M. J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32, 231–253 (1991).

J. L. Jackel, E. M. Vogel, J. S. Aitchinson, “Ion exchanged optical waveguides for all-optical switching,” Appl. Opt. 29, 3126–3129 (1990).
[CrossRef] [PubMed]

Weber, M. J.

E. M. Vogel, M. J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32, 231–253 (1991).

Ann. Chim. Sci. Mater. (1)

E. Fargin, A. Berthereau, T. Cardinal, J. J. Videau, A. Villesuzanne, G. Le Flem, “Contribution of theoretical chemistry to investigation of optical non linearities in glasses,” Ann. Chim. Sci. Mater. 23, 27–32 (1998).
[CrossRef]

Appl. Opt. (2)

Eur. J. Solid State Inorg. Chem. (2)

T. Cardinal, E. Fargin, G. Le Flem, L. Canioni, P. Segonds, L. Sarger, F. Adamietz, A. Ducasse, “Nonlinear optical properties of glasses of the NaPO3–Na2B4O7–TiO2 system,” Eur. J. Solid State Inorg. Chem. 31, 935–941 (1994).

T. Cardinal, E. Fargin, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, A. Ducasse, F. Adamietz, “Nonlinear optical properties of some niobium (V) oxide glasses,” Eur. J. Solid State Inorg. Chem. 33, 597–605 (1996).

J. Lightwave Technol. (3)

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

K. S. Chiang, “Construction of refractive index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

M. Guntau, A. Brauer, W. Karthe, T. Possner, “Numerical simulation of ion exchange in glass for integrated optical components,” J. Lightwave Technol. 10, 312–315 (1992).
[CrossRef]

J. Phys. Chem. (1)

R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
[CrossRef]

J. Quantum Electron. (1)

P. J. R. Laybourn, G. Steward, “Fabrication of ion exchanged optical waveguides from dilute silver nitrate melts,” J. Quantum Electron. QE-14, 930–934 (1978).

Phys. Chem. Glasses (2)

E. M. Vogel, M. J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32, 231–253 (1991).

A. A. Ahmed, E. W. Abdallah, “Effect of ion exchange and heat treatment conditions on the diffusion of silver into a soda-lime-silica glass,” Phys. Chem. Glasses 38, 42–50 (1997).

Phys. Status Solidi A (1)

J. F. Ducel, J. J. Videau, K. S. Suh, J. Sénégas, “Influence of calcium-hydroxyapatite on sodium borophosphate glasses. 31P and 11B NMR investigations,” Phys. Status Solidi A 144, 23–30 (1994).
[CrossRef]

Other (1)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 408–412.

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Figures (9)

Fig. 1
Fig. 1

Examples of exchange profiles calculated from Eq. (1) (see text) for diffusion coefficient D = 1 µm2 mn-1 with Steward coefficients α = 0.01 (close to an erfc) and α = 0.9 and α = 0.99 (close to a Heaviside function). Comparison with exchange profiles for diffusion coefficient D = 2 µm2 mn-1 with Steward coefficient α = 0.9.

Fig. 2
Fig. 2

Visible–near infrared absorption coefficient spectra of an x = 0 glass sample (thickness, 1.03 cm) together with optical loss (P) and absorption (α) values for typical telecommunication wavelengths.

Fig. 3
Fig. 3

Concentration of Ag+ ions at the surface of the glass with composition x = 0.468 after exchange during 30 min at 360 °C versus molar fraction y of AgNO3 in the compositional molten bath yAgNO3–(1 - y)NaNO3. The curve is a guide for the eye. The saturation step corresponds to Na+ concentration in glass (see Table 1).

Fig. 4
Fig. 4

Refractive index and Ag+ concentration (inset) profiles of x = 0.36 compositional glasses after exchange durations of 30, 120 and 240 min. The curves are guides for the eye.

Fig. 5
Fig. 5

Normalized diffusion profiles of Ag+ ion concentration in relation to the glass surface concentration (C 0) of the glass samples for values of x shown. The curves are fit curves (see text and Table 2).

Fig. 6
Fig. 6

Normalized diffusion profiles of Ag+ ion concentration in relation to the glass surface concentration (C 0) of glass samples with x = 0 for an exchange time of 22 h.

Fig. 7
Fig. 7

Variation of Ag+ and Na+ diffusion and Steward (inset) coefficients as a function of molar fraction x of Ca(PO3)2 in the glasses. The curves are guides for the eye.

Fig. 8
Fig. 8

Evolution of glass-transition and -crystallization temperatures as a function of molar fraction x of Ca(PO3)2 in the glasses. The curves are guides for the eye.

Fig. 9
Fig. 9

Comparison of normalized diffusion profiles of Ag+ ion concentration with glass surface concentration (C 0) and normalized refractive-index step profiles after exchange durations of 30 and 240 min. The curves are guides for the eye.

Tables (2)

Tables Icon

Table 1 Sodium Concentration and Glass-Transition and -Crystallization Temperatures of the (0.665-x)NaPO3 + xCa(PO3)2 + 0.035Na2B4O7 + 0.300Nb2O5 Glass Samples

Tables Icon

Table 2 Steward Coefficient (α) and Ag+ (D Ag) and Na+ (D Na) Diffusion Coefficient Values for Glass Samples for Several Ion-Exchange Times As Obtained from Ag+ Concentration Profiles or WKB Analysis

Equations (2)

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

t C=DAg1-αC 2C+αDAg1-αC2C2,
Cz, t=C0 erfcz2DAgt,

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