Abstract

When the tip of a fluoride glass fiber is exposed to ambient air, water vapor reacts with the glass constituents, increasing the OH contaminants at the surface. These OH impurities then diffuse inside the glass according to Fick’s laws. Laser radiation at around 3µm is strongly absorbed by the OH contaminants, causing local heating of the fiber tip resulting in an increase of the diffusion process which ultimately leads to fiber tip destruction. We accurately model this phenomenon by combining the diffusion theory with a basic thermal equation. Experimental measurements are in agreement with the model predictions for a good range of operating conditions.

©2012 Optical Society of America

1. Introduction

The diffusion of various gases in silica has been studied and fairly well understood for a long time. In particular, the diffusion and solubility of water vapor in bulk silica glass have been well characterized [1]. Among the most notable results, a theoretical model of the temperature and pressure dependence of the solubility of gasses has been developed by Studt et al. for non-reacting [2] and reacting species [3].

Fluoride glasses are known to be highly reactive with liquid water. It has been discovered that three processes occur when water contacts ZBLAN [4]: the glass constituents dissolve, water penetrates the matrix and crystals grow at the surface [5,6]. Simmons et al. studied the first process extensively [7]. The variation of constituents with depth has also been a recurring subject of research [8] as well as the study of the exposed surface composition [9]. The second process (OH diffusion) can be explained by the formation of Zr-OH and La-OH groups [10].

Some fluoride glass compositions are known to be more permeable than others. Trégoat et al. [11] and Simmons [12] found thorium glass to be more robust to water exposure. However, since this element is radioactive, its usage has been banned for safety reasons. More popular candidates nowadays are AlF3- based glasses. These glasses were found to be at least ten times more stable than the more common ZrF4- based compositions [13].

The corrosion process is faster in a low pH solution [14]. The deterioration can be enhanced hundreds or even thousands of times with low pH. This observation is without any doubt crucial to understanding the difference between exposure to condensing and non-condensing humidity. In contrast with the astounding amount of work that has been done for liquid water exposure, little information is available on noncondensing water vapor effects. Robinson et al. [15] pointed out that no visual corrosion is observed with water vapor at temperatures up to 200°C, whereas their glass samples were almost immediately crystallized when exposed to liquid water. Simmons et al. confirmed this observation in [7].

The most comprehensive study on water vapor-induced fluoride glass deterioration was realized by Trégoat et al. [16]. They exposed a BZnYbT fluoride glass sample to water vapor for 22.5 hours at 344°C. After cooling, the variation of the 2.9µm absorption band was measured after successively removing thin layers of material by polishing the sample. Using Fick’s laws of diffusion, they were able to predict accurately the absorbance as a function of depth.

In recent years, the development of high power 3 μm fiber lasers has been in effervescence [17], but its development has been hindered by this fiber tip degradation phenomenon. Various authors have suggested the use of an ultra-pure nitrogen flux directed at the fiber tip [18,19] or the use of end-caps [20] to mitigate or slow down this corrosion process. In some cases, the fiber tip was indeed observed to undergo a catastrophic thermal runaway after only a few minutes of laser operation. This phenomenon is specific to these lasers because their emission wavelength is centered on the highly absorptive resonance of OH contaminants coming from the atmosphere. After these species are absorbed by the glass structure, they simply diffuse according to Fick’s laws. As the total number of contaminants increase, laser absorption follows the same rising trend. As a result, the temperature of the fiber also increases, which in turn has an effect on the speed of the diffusion process, and so on. This positive feedback loop ultimately leads to the catastrophic destruction of the fiber tip. In this paper we show that, by a proper modeling of this catastrophic photo-induced corrosion phenomenon, we are able to predict the time of failure of the fiber tip for a given set of ambient conditions.

2. Theory

The OH diffusion process at the fiber tip is schematized in Fig. 1 .

 

Fig. 1 Schematic representation of the fiber degradation phenomenon.

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The first step in developing the theoretical model is to apply Fick's laws to this situation. The one dimensional solution for an infinite reservoir of the contaminant is well known [16]. Considering the total number of contaminants per unit of transverse surface, the time dependent solution at constant temperature is given by Eq. (1)

N(t)=0C(x)dx=2πC(0)D(T)t
whereC(0) is the concentration at the interface (also called the solubility) and D(T) is the temperature dependent diffusion coefficient. The x-axis is shown in Fig. 1. The more general case of a variable temperature will be considered next. The diffusion coefficient is known to follow an Arrhenius temperature dependence [1].
D(t)=D0exp[EaRT]
R is the perfect gas constant, with a value of 8.3144Jmol-1K-1, Ea is the activation energy associated with D0, the diffusion at infinite temperature. The solubility C(0) can also be temperature dependent, but we assume a fixed value in this model. Equations (1) and (2) are readily combined into Eq. (3).
N(t)=2πC(0)D0exp[EaRT]t
This relation is valid for a fixed temperature. When the temperature varies with time, it can be shown that the total number of contaminants is rather expressed using the following version.
N(t)=2πC(0)D0exp[EaRT(t)]dt
A thermal model is needed to link this result with the fiber tip temperature. The Beer-Lambert law (see Ref [21].) in the limit of small absorption is a valid simplification for this situation.
T(t)Tamb=Rth(1exp[ε(λ)N(t)])P0Rthε(λ)N(t)P0
ε is the molar absorption coefficient (defined in base e), which is resonantly wavelength dependent. Rth is the thermal resistance between the fiber tip and the ambient temperature Tamb. P0 is the incident laser power. Equations (4) and (5) can be combined to get:
T(t)Tamb=2πRthε(λ)P0C(0)D0exp[EaRT(t)]dt
The integral is then isolated.
exp[EaRT(t)]dt=π(2D0Rthε(λ)P0C(0))2(T(t)Tamb)2
The time derivative is taken on both sides of Eq. (7).
exp[EaRT(t)]=2π(2D0Rthε(λ)P0C(0))2(T(t)Tamb)dTdt
dt=π2(D0Rthε(λ)P0C(0))2(T(t)Tamb)exp[EaRT(t)]dT
Finally, time is integrated from time zero, i.e. the beginning of the laser emission (when the fiber tip is at Tamb) to the time t corresponding to a temperature T.

t=π2(D0RthP0ε(λ)C(0))2TambT(TTamb)exp[EaRT]dT

The Eq. (10) can be used directly to predict the duration of a fiber tip for a given set of conditions. The lifetime can be defined as the time required to reach a critical temperature, for example 100°C (373K). Note that the solution of the integral only depends on the ambient temperature and the activation energy.

A few interesting observations arise from this theoretical model. According to Eq. (10), the lifetime is proportional to the inverse square of the laser power. Power scaling can therefore be extremely impeded by this degradation phenomenon. , the thermal resistance, can be high if natural convection is used to cool the fiber tip, as is the case in this paper. However, it is also possible to use a more aggressive cooling technique to significantly increase the lifetime. Thermal conduction can easily be ten times better than natural convection. According to Eq. (10), a tenfold decrease in thermal resistance would increase the lifetime by a factor of one hundred. It is consequently easy to understand the importance of good thermal design when dealing with this phenomenon.

The tip lifetime dependence on ambient temperature is somehow more complex to analyze. The integral in Eq. (10) must be solved for different values of Tamb to understand its effect. This information can be of upmost importance when designing a laser that can be exposed to a wide range of ambient conditions. Additionally, a higher ambient temperature can be used for accelerated aging, especially with materials which are more impermeable than standard fluoride glass, in which case the time before failure can be prohibitively long. Figure 2 depicts the influence of ambient temperature on the fiber tip lifespan for several activation energies. In first approximation, the relation is almost exponential. As can be seen, the tip degradation is more sensitive to the increase of ambient temperature for higher values of Ea.

 

Fig. 2 Influence of the ambient temperature for a constant output power. The durations are normalized with respect to the tip lifetime for an ambient temperature of 20°C.

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3. Experiment

We proceeded to a set of measurements of the fiber tip temperature increase as a function of time in order to confirm the validity of our model. A monolithic Er:ZBLAN fiber laser operating at 2825 nm was used. See Ref [20]. for detail. We replaced the endcap by a 1.3 meter segment of 220/240μm (core/cladding) 0.22NA multimode fluoride glass fiber made by Le Verre Fluoré (IRGUIDE 220/250-20). Between each experiment, the fiber tip was cleaved at about one centimeter away from the acrylate polymer jacket. The fiber was then installed in an aluminium v-groove, with the tip protruding by about one centimeter. Natural convection is the only significant means of cooling in this arrangement. At high temperatures, however, thermal radiation becomes non-negligible, and the model is expected to become less accurate.

The thermal resistance Rth depends on the fiber diameter, but we used the same 240µm fiber for all our measurements. This parameter is therefore considered constant in the following. It is also important to note that the transverse thermal gradient inside the fiber is very small (on the order of a few tenths of a degree). The natural convection thermal resistance is much higher than the transverse conduction within the fiber, justifying the approximation of a constant temperature across the fiber tip cross section.

During the experiment, the room relative humidity was maintained at 50 ± 5%. The fiber tip temperature was monitored using a thermal camera (Jenoptik, Variocam) with a close-up lens. The spatial resolution was 50µm with a 5 s delay between each measurement. We used an emissivity of 0.8 for the fiber. The output power was noted at the beginning of the experiment. There was no significant loss until the very last seconds of the test, and therefore the power was not recorded during the experiments.

We observed that the fiber tip was actually not at room temperature at the beginning (i.e. first recorded value) of the tests. To explain this, we hypothesized that imperfections at the cleaved surface could account for an initial and intrinsic absorption of a few milliwatts of laser power. These initial losses can be reckoned with by assuming a higher ambient temperature in Eq. (10).

Figure 3 shows a set of curves obtained using this technique. The solid red curves correspond to the theoretical predictions. The experimental data were filtered using a 100s moving average to remove the higher frequency noise.

 

Fig. 3 Temporal temperature evolution of the fiber tip for several output powers. The solid curves are the theoretical predictions and the dots are the experimental data.

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4. Discussion

The curves in Fig. 3 provide good evidence of the validity and accuracy of the proposed model, especially in predicting fiber tip lifetime. In fact, the general shape of the temperature temporal evolution is also predicted with very good accuracy. Evidently, the values of the unknown material parameters Ea and D0εC(0) have first to be found in order to plot the theoretical curves in Fig. 3. Their estimation could be achieved by simply minimizing the error between one of the theoretical curve and Eq. (10). This direct approach can be tedious because of the nonlinearities of the integral. An easier method is to define a critical time tcrand temperature Tcr pair for one of the experimental curves. For each value of Ea to be evaluated, the corresponding value of D0RthεC(0) is then calculated with Eq. (11).

D0RthεC(0)=π21tcrP0TambTcr(TTamb)exp[EaRT]dT

Using this method, the theoretical curve is guaranteed to cross the temperature at time . A least squares figure of merit is then used to minimize the difference between the theoretical curve and the experimental data. Figure 4 illustrates this iterative process. Using this method, we found Ea=114.5kJ/mol and D0εC(0)Rth=1.03×108KW-1s-1/2. This set of two values was used to fit the six curves shown in Fig. 3.

 

Fig. 4 Determination of the material parameters. tcr=12h and Tcr=80°C for this example.

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It is important to note that ε, and consequently the product D0εC(0), are highly wavelength dependent. We thus emphasize the fact that the values derived here are associated with a laser wavelength of 2825 nm. Also note that based on the set of temperature curves only, there is no way to ascertain the individual values of D0, ε and C(0): only their product can be determined. Other experiments should be performed in addition to this one to lift this uncertainty. Measuring the absorbance as a function of depth, as proposed by Trégoat et al. [16] can provide the diffusion coefficient. A modified Seiverts method [3] could provide the solubility. For this experiment, the sample is inserted in a sealed chamber with a water vapor atmosphere. The pressure is first measured at the beginning of the experiment and then again when the sample is saturated with water vapor. The solubility is inferred by calculating the amount of water vapor dissolved in the sample.

An alternative experiment could be achieved by maintaining a constant laser power while varying the ambient temperature. This could be realized easily using an environmental chamber, for example. It would be desirable to use this “accelerated aging” variant to predict the endcap lifetime at lower temperature for materials more impermeable than standard fluoride glass.

During this experiment, the relative humidity was maintained almost constant. As mentioned before, the solubility of a monoatomic non-reacting gas was found by Studt et al. to be proportional to the pressure [2] and the square root of pressure in the case of a reacting gas [3]. The latter is more probable for water vapor interacting with fluoride glass. We would therefore expect the fiber tip lifetime to be inversely proportional to relative humidity since Eq. (10) predicts an inverse square proportionality with respect to solubility. This hypothesis is admittedly speculative, since the results in [2] and [3] were only valid for a monoatomic gas.

5. Conclusion

We have proposed a new model for the fiber temperature runaway phenomenon observed with fiber lasers operating near 3µm. The fiber tip duration is predicted by our analytical solution to be proportional to the inverse square of the laser power. A similar dependence links the lifetime with the thermal resistance. The model also forecasts an almost exponential influence of the ambient temperature on the fiber tip duration.

Acknowledgments

This research was supported by the Canadian Institute for Photonic Innovations (CIPI), the Fonds de recherche du Québec - Nature et technologies (FRQNT), the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Foundation for Innovation (CFI). The authors are grateful to Marcel Poulain for his useful insights.

References and links

1. A. J. Moulson and J. P. Roberts, “Water in silica glass,” Trans. Faraday Soc. 57, 1208–1216 (1961). [CrossRef]  

2. P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970). [CrossRef]  

3. J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972). [CrossRef]  

4. R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985). [CrossRef]  

5. R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984). [CrossRef]  

6. C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982). [CrossRef]  

7. C. J. Simmons and J. H. Simmons, “Chemical durability of fluoride glasses: I, reaction of fluorozirconate glasses with water,” J. Am. Ceram. Soc. 69(9), 661–669 (1986). [CrossRef]  

8. B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999). [CrossRef]  

9. A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004). [CrossRef]  

10. M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988). [CrossRef]  

11. D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986). [CrossRef]  

12. C. J. Simmons, “Chemical durability of fluoride glasses: II, reaction of barium-thorium-based glasses with water,” J. Am. Ceram. Soc. 70(4), 295–300 (1987). [CrossRef]  

13. G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001). [CrossRef]  

14. C. J. Simmons, “Chemical durability of fluoride glasses: III, the effect of solution pH,” J. Am. Ceram. Soc. 70(9), 654–661 (1987). [CrossRef]  

15. M. Robinson and M. G. Drexhage, “A phenomenological comparison of some heavy metal fluoride glasses in water environments,” Mater. Res. Bull. 18(9), 1101–1112 (1983). [CrossRef]  

16. D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

17. S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012). [CrossRef]  

18. M. Bernier, D. Faucher, N. Caron, and R. Vallée, “Highly stable and efficient erbium-doped 2.8 μ all fiber laser,” Opt. Express 17(19), 16941–16946 (2009). [CrossRef]   [PubMed]  

19. S. Tokita, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “12 W Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Lett. 36(15), 2812–2814 (2011). [CrossRef]   [PubMed]  

20. D. Faucher, M. Bernier, N. Caron, and R. Vallée, “Erbium-doped all-fiber laser at 2.94 microm,” Opt. Lett. 34(21), 3313–3315 (2009). [CrossRef]   [PubMed]  

21. J. P. Bromberg, Physical Chemistry, 2nd ed. (Allyn and Bacon, 1984), p. 949.

References

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  1. A. J. Moulson and J. P. Roberts, “Water in silica glass,” Trans. Faraday Soc. 57, 1208–1216 (1961).
    [Crossref]
  2. P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970).
    [Crossref]
  3. J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972).
    [Crossref]
  4. R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
    [Crossref]
  5. R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
    [Crossref]
  6. C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
    [Crossref]
  7. C. J. Simmons and J. H. Simmons, “Chemical durability of fluoride glasses: I, reaction of fluorozirconate glasses with water,” J. Am. Ceram. Soc. 69(9), 661–669 (1986).
    [Crossref]
  8. B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
    [Crossref]
  9. A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
    [Crossref]
  10. M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988).
    [Crossref]
  11. D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
    [Crossref]
  12. C. J. Simmons, “Chemical durability of fluoride glasses: II, reaction of barium-thorium-based glasses with water,” J. Am. Ceram. Soc. 70(4), 295–300 (1987).
    [Crossref]
  13. G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001).
    [Crossref]
  14. C. J. Simmons, “Chemical durability of fluoride glasses: III, the effect of solution pH,” J. Am. Ceram. Soc. 70(9), 654–661 (1987).
    [Crossref]
  15. M. Robinson and M. G. Drexhage, “A phenomenological comparison of some heavy metal fluoride glasses in water environments,” Mater. Res. Bull. 18(9), 1101–1112 (1983).
    [Crossref]
  16. D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).
  17. S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).
    [Crossref]
  18. M. Bernier, D. Faucher, N. Caron, and R. Vallée, “Highly stable and efficient erbium-doped 2.8 μ all fiber laser,” Opt. Express 17(19), 16941–16946 (2009).
    [Crossref] [PubMed]
  19. S. Tokita, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “12 W Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Lett. 36(15), 2812–2814 (2011).
    [Crossref] [PubMed]
  20. D. Faucher, M. Bernier, N. Caron, and R. Vallée, “Erbium-doped all-fiber laser at 2.94 microm,” Opt. Lett. 34(21), 3313–3315 (2009).
    [Crossref] [PubMed]
  21. J. P. Bromberg, Physical Chemistry, 2nd ed. (Allyn and Bacon, 1984), p. 949.

2012 (1)

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).
[Crossref]

2011 (1)

2009 (2)

2004 (1)

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

2001 (1)

G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001).
[Crossref]

1999 (1)

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

1988 (1)

M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988).
[Crossref]

1987 (2)

C. J. Simmons, “Chemical durability of fluoride glasses: II, reaction of barium-thorium-based glasses with water,” J. Am. Ceram. Soc. 70(4), 295–300 (1987).
[Crossref]

C. J. Simmons, “Chemical durability of fluoride glasses: III, the effect of solution pH,” J. Am. Ceram. Soc. 70(9), 654–661 (1987).
[Crossref]

1986 (2)

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

C. J. Simmons and J. H. Simmons, “Chemical durability of fluoride glasses: I, reaction of fluorozirconate glasses with water,” J. Am. Ceram. Soc. 69(9), 661–669 (1986).
[Crossref]

1985 (2)

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

1984 (1)

R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
[Crossref]

1983 (1)

M. Robinson and M. G. Drexhage, “A phenomenological comparison of some heavy metal fluoride glasses in water environments,” Mater. Res. Bull. 18(9), 1101–1112 (1983).
[Crossref]

1982 (1)

C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
[Crossref]

1972 (1)

J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972).
[Crossref]

1970 (1)

P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970).
[Crossref]

1961 (1)

A. J. Moulson and J. P. Roberts, “Water in silica glass,” Trans. Faraday Soc. 57, 1208–1216 (1961).
[Crossref]

Bansal, N. P.

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
[Crossref]

Bernier, M.

Bradner, T.

R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
[Crossref]

Burman, C.

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

Caron, N.

Craievich, A. F.

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

Dersch, O.

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

Doremus, R. H.

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
[Crossref]

Drexhage, M. G.

M. Robinson and M. G. Drexhage, “A phenomenological comparison of some heavy metal fluoride glasses in water environments,” Mater. Res. Bull. 18(9), 1101–1112 (1983).
[Crossref]

Faucher, D.

Fonteneau, G.

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

Frischat, G. H.

G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001).
[Crossref]

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

Fulrath, R. M.

J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972).
[Crossref]

P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970).
[Crossref]

Hammer, P.

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

Hashida, M.

Hueber, B.

G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001).
[Crossref]

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

Jackson, S. D.

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).
[Crossref]

Lanford, W. A.

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

Le Toullec, M.

M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988).
[Crossref]

Liepmann, M. J.

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

Lucas, J.

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

Mackenzie, J. D.

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

Maldener, A.

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

Messaddeq, Y.

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

Moulson, A. J.

A. J. Moulson and J. P. Roberts, “Water in silica glass,” Trans. Faraday Soc. 57, 1208–1216 (1961).
[Crossref]

Moynihan, C. T.

D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

Murakami, M.

Murphy, D.

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
[Crossref]

Pulcinelli, S. H.

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

Ramdohr, B.

G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001).
[Crossref]

Rauch, F.

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

Rizzato, A. P.

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

Roberts, J. P.

A. J. Moulson and J. P. Roberts, “Water in silica glass,” Trans. Faraday Soc. 57, 1208–1216 (1961).
[Crossref]

Robinson, M.

M. Robinson and M. G. Drexhage, “A phenomenological comparison of some heavy metal fluoride glasses in water environments,” Mater. Res. Bull. 18(9), 1101–1112 (1983).
[Crossref]

Sakabe, S.

Santilli, C. V.

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

Shackelford, J. F.

J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972).
[Crossref]

P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970).
[Crossref]

Shimizu, S.

Simmons, C. J.

M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988).
[Crossref]

C. J. Simmons, “Chemical durability of fluoride glasses: III, the effect of solution pH,” J. Am. Ceram. Soc. 70(9), 654–661 (1987).
[Crossref]

C. J. Simmons, “Chemical durability of fluoride glasses: II, reaction of barium-thorium-based glasses with water,” J. Am. Ceram. Soc. 70(4), 295–300 (1987).
[Crossref]

C. J. Simmons and J. H. Simmons, “Chemical durability of fluoride glasses: I, reaction of fluorozirconate glasses with water,” J. Am. Ceram. Soc. 69(9), 661–669 (1986).
[Crossref]

C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
[Crossref]

Simmons, J. H.

M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988).
[Crossref]

C. J. Simmons and J. H. Simmons, “Chemical durability of fluoride glasses: I, reaction of fluorozirconate glasses with water,” J. Am. Ceram. Soc. 69(9), 661–669 (1986).
[Crossref]

C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
[Crossref]

Studt, P. L.

J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972).
[Crossref]

P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970).
[Crossref]

Sutter, H.

C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
[Crossref]

Tokita, S.

Tran, D. C.

C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
[Crossref]

Tregoat, D.

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

Trégoat, D.

D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

Vallée, R.

J. Am. Ceram. Soc. (5)

C. J. Simmons and J. H. Simmons, “Chemical durability of fluoride glasses: I, reaction of fluorozirconate glasses with water,” J. Am. Ceram. Soc. 69(9), 661–669 (1986).
[Crossref]

M. Le Toullec, C. J. Simmons, and J. H. Simmons, “Infrared spectroscopic studies of the hydrolysis reaction during leaching of heavy-metal fluoride glasses,” J. Am. Ceram. Soc. 71(4), 219–224 (1988).
[Crossref]

C. J. Simmons, “Chemical durability of fluoride glasses: II, reaction of barium-thorium-based glasses with water,” J. Am. Ceram. Soc. 70(4), 295–300 (1987).
[Crossref]

C. J. Simmons, “Chemical durability of fluoride glasses: III, the effect of solution pH,” J. Am. Ceram. Soc. 70(9), 654–661 (1987).
[Crossref]

D. Trégoat, G. Fonteneau, C. T. Moynihan, and J. Lucas, “Surface -OH profile from reaction of a heavy-metal fluoride glass with atmospheric water,” J. Am. Ceram. Soc. 68, 171–173 (1985).

J. Appl. Phys. (2)

P. L. Studt, J. F. Shackelford, and R. M. Fulrath, “Solubility of gases in glass-a monatomic model,” J. Appl. Phys. 41(7), 2777–2780 (1970).
[Crossref]

J. F. Shackelford, P. L. Studt, and R. M. Fulrath, “Solubility of gases in glass. II. He, Ne, and H2 in fused silica,” J. Appl. Phys. 43(4), 1619–1626 (1972).
[Crossref]

J. Mater. Sci. (1)

R. H. Doremus, D. Murphy, N. P. Bansal, W. A. Lanford, and C. Burman, “Reaction of zirconium fluoride glass with water: kinetics of dissolution,” J. Mater. Sci. 20(12), 4445–4453 (1985).
[Crossref]

J. Mater. Sci. Lett. (1)

R. H. Doremus, N. P. Bansal, T. Bradner, and D. Murphy, “Zirconium fluoride glass: surface crystals formed by reaction with water,” J. Mater. Sci. Lett. 3(6), 484–488 (1984).
[Crossref]

J. Non-Cryst. Solids (4)

D. Tregoat, M. J. Liepmann, G. Fonteneau, J. Lucas, and J. D. Mackenzie, “Comparative corrosion mechanism of ThF4 and ZrF4 based fluoride glasses in aqueous solutions,” J. Non-Cryst. Solids 83(3), 282–296 (1986).
[Crossref]

B. Hueber, G. H. Frischat, A. Maldener, O. Dersch, and F. Rauch, “Initial corrosion stages of a heavy metal fluoride glass in water,” J. Non-Cryst. Solids 256–257, 130–134 (1999).
[Crossref]

A. P. Rizzato, C. V. Santilli, S. H. Pulcinelli, Y. Messaddeq, A. F. Craievich, and P. Hammer, “Study on the initial stages of water corrosion of fluorozirconate glasses,” J. Non-Cryst. Solids 348, 38–43 (2004).
[Crossref]

G. H. Frischat, B. Hueber, and B. Ramdohr, “Chemical stability of ZrF4- and AlF3- based heavy metal fluoride glasses in water,” J. Non-Cryst. Solids 284(1-3), 105–109 (2001).
[Crossref]

Mater. Res. Bull. (2)

M. Robinson and M. G. Drexhage, “A phenomenological comparison of some heavy metal fluoride glasses in water environments,” Mater. Res. Bull. 18(9), 1101–1112 (1983).
[Crossref]

C. J. Simmons, H. Sutter, J. H. Simmons, and D. C. Tran, “Aqueous corrosion studies of a fluorozirconate glass,” Mater. Res. Bull. 17(9), 1203–1210 (1982).
[Crossref]

Nat. Photonics (1)

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Trans. Faraday Soc. (1)

A. J. Moulson and J. P. Roberts, “Water in silica glass,” Trans. Faraday Soc. 57, 1208–1216 (1961).
[Crossref]

Other (1)

J. P. Bromberg, Physical Chemistry, 2nd ed. (Allyn and Bacon, 1984), p. 949.

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Figures (4)

Fig. 1
Fig. 1 Schematic representation of the fiber degradation phenomenon.
Fig. 2
Fig. 2 Influence of the ambient temperature for a constant output power. The durations are normalized with respect to the tip lifetime for an ambient temperature of 20°C.
Fig. 3
Fig. 3 Temporal temperature evolution of the fiber tip for several output powers. The solid curves are the theoretical predictions and the dots are the experimental data.
Fig. 4
Fig. 4 Determination of the material parameters. t cr =12h and T cr =80°C for this example.

Equations (11)

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

N( t )= 0 C( x )dx = 2 π C( 0 ) D( T )t
D( t )= D 0 exp[ E a RT ]
N( t )= 2 π C( 0 ) D 0 exp[ E a RT ]t
N( t )= 2 π C( 0 ) D 0 exp[ E a RT( t ) ]dt
T( t ) T amb = R th ( 1exp[ ε( λ )N( t ) ] ) P 0 R th ε( λ )N( t ) P 0
T( t ) T amb = 2 π R th ε( λ ) P 0 C( 0 ) D 0 exp[ E a RT( t ) ]dt
exp[ E a RT( t ) ]dt = π ( 2 D 0 R th ε( λ ) P 0 C( 0 ) ) 2 ( T( t ) T amb ) 2
exp[ E a RT( t ) ]= 2π ( 2 D 0 R th ε( λ ) P 0 C( 0 ) ) 2 ( T( t ) T amb ) dT dt
dt= π 2 ( D 0 R th ε( λ ) P 0 C( 0 ) ) 2 ( T( t ) T amb )exp[ E a RT( t ) ]dT
t= π 2 ( D 0 R th P 0 ε( λ )C( 0 ) ) 2 T amb T ( T T amb )exp[ E a RT ]dT
D 0 R th εC( 0 )= π 2 1 t cr P 0 T amb T cr ( T T amb )exp[ E a RT ]dT

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