] O U R N A L OF
Journal of Non-Crystalline Solids 177 (1994) 427-431
Low-temperature deformation of fluoride and oxide glass fibers below their glass transition temperatures Manabu Koide *, Ryuji Sato, Takayuki Komatsu, Kazumasa Matusita Department of Chemistry, Nagaoka Universityof Technology, Kamitomioka-cho, Nagaoka 940-21, Japan
Abstract Deformations of some fluoride and oxide glass fibers were measured at temperatures below their glass transition temperatures. Glass fibers were wound on a cylinder, kept at low temperatures for various times and the remaining strains of fibers after the heat treatment were measured. It was found that the temperature region in which fluoride glass fibers are deformed is much lower than that for oxide glass fibers. The deformation mechanisms of each of the glass fibers were analyzed based on a log-normal distribution model of relaxation times. It was found that the activation energy for low-temperature deformation is much lower than that for viscous flow near the glass transition temperature. It was concluded that the deformations of each of the glass fibers are caused by different relaxation mechanisms.
1. Introduction Usually, a glass is rigid and brittle below the glass transition t e m p e r a t u r e and deformation of glasses occurs above the glass transition temperature. However, it was reported that it is possible to deform glasses by external pressure and by an electric field even at temperatures below the glass transition region [1-3]. Glass fibers are used widely, such as in optical communication systems and in laser b e a m transmission for surgery. Therefore, stable physical and chemical properties of glass fibers are desired under all conditions. Fluoride glasses are promising materials for the development of ultralow-loss I R waveguides and are expected to have possible application in
* Corresponding author. Tel: +81-258 46 6000. Telefax: + 81-258 46 6507.
optical fiber communication . Therefore, properties (such as fiber strength) and coatings have been studied by many researchers [5,6]. In this study, the deformations of fluoride glass fibers and some oxide glass fibers were measured at temperatures below the glass transition temperature, and the relaxation mechanisms of deformation were analyzed by a l o g - n o r m a l distribution model in relaxation times.
2. Theory and analytical procedures of deformation A schematic diagram of the m e a s u r e m e n t procedure is given in Fig. 1. Glass fibers were wound on a cylinder of diameter, R 0, and kept at a t e m p e r a t u r e below the glass transition for various times. Then the fibers were released from the cylinder and the remaining strains were mea-
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M. Koide et al. /Journal of Non-Crystalline Solids 177 (1994) 427-431
~(tr) to fiber
Fig. 1. Schematic diagram of measurement procedure for fiber deformation.
sured. Fig. 2 shows the method of strain measurement of deformed fibers. For bent fibers, compressive and tensile stresses were produced respectively at the inside and outside of a bent fiber. The stretch deformation of a fiber is largest at the outside surface of the fiber, as shown in Fig. 2. The strain, e, of glass fibers at a distance R + r from the bending center can be represented by e = r/R,
where R is the bending radius and r is the distance from the center line of the fiber. As is indicated by Eq. (1), the biggest stretch deformation can be calculated from the fiber's radius and its bending radius. To estimate the stress, it was assumed that the elastic deformation obeys Hooke's law and that the elastic moduli of the glass fibers are constant, irrespective of the tensile or compressive stress. It is considered that the stress relaxation causes deformation of glass fibers. The stress decreases with time with a fixed strain, e 0, as shown in Fig. 3. Before the fiber is released from the cylinder at the time, tr, the
Fig. 3. The relaxation function in the stress relaxation model.
change of stress, tr, with time can be expressed as follows in a system with a single relaxation time: dtr/dt = -tr/~'. Eq. (2) is integrated to give tr = tr0 e x p ( - t / r ) ,
i - - i
21t(R4-r)de Fig. 2. Method of strain measurement of deformed fiber.
where tr0 is the initial stress, 7 is the relaxation time and t is the time. After the fiber is released, the strain e(t r) = ~b(tr)e 0 remains. The relaxation function, ~b(tr), is defined as follows and illustrated schematically in Fig. 3: ~b(tr) = ( R o / R ( t r ) ) ,
where R (t r) is the bending radius in the released state after heat treatment for time t r and R 0 is the cylinder's radius. With Hooke's law expressed as tr(t r) = G(1 - ~O(tr))e0, where G is the elastic constant, Eq. (2) can be written as ] -- q / ( t r ) =
exp( --tr/~" ) .
Mackenzie  reported that the relaxation behavior of the deformation of some fluoride glass fibers is expressed by Eq. (5), indicating a single relaxation time. In case the relaxation time spectrum is expressed as a distribution function, the relaxation mechanism can be analyzed by a nonlinear relaxation function, and this non-linear re-
M. Koide et al. /Journal of Non-Crystalline Solids 177 (1994) 427-431
laxation process is expressed very well by the Kohlrausch-Williams-Watt (KWW) equation : 1 - ~ b ( / r ) = e x p ( - ( t / r ) n)
where n is the distribution parameter. If n is taken as 1, the KWW equation corresponds with Eq. (3). It is known that the relaxation time is distributed more diffusely as n approaches zero. Further, it is possible to fit the temperature dependence of the relaxation times with the Arrehenius behavior,
r = ro exp(E/kT),
• $iO 2 f i b e r a g e doped f i b e r • F doped f i b e r Annealing t i m e = 24h
0.5 t:n o
where E is an activation energy for relaxation and k is the Boltzmann constant.
1.0 1000 / T
1.1 ( K-' )
Fig. 4. Relation between bending radius and heat treatment. Lines are drawn as guides for the eye.
analyzed based on the non-linear relaxation function (6).
3. Experimental procedure The chemical composition and diameter of the glass fibers used in this study are shown in Table 1. SiO2 glass fiber is a single fiber system in which the chemical composition and refractive index are uniform in the fiber. However, other glass fibers are optical fibers, consisting of core and cladding. The fluoride glass fiber is a ZrF4based system and one of the most stable heavymetal fluoride glasses. The glass fibers of diameter 125, 200 and 300 ~ m were wound around the cylinders of radius 3.0, 4.5 and 9.5 cm, respectively. Quartz glass and alumina tubes were used as cylinders. Subsequently, these fibers were annealed at various temperatures and times. After annealing, the fibers were released and the bending radii of the deformed fibers were measured. The relative bending radius changes were calculated as a function of the annealing temperature and time. The stress relaxation phenomena were
Table 1 Chemical composition and diameter of glass fibers Glass fiber
SiO 2 glass fiber Ge-doped SiO 2 glass fiber F-doped SiO 2 glass fiber Fluoride glass fiber
200 125 125 300
4. Results Fig. 4 shows the relation between the bending radius of deformed fibers and the annealing temperature after 24 h annealing. Here, R 0 is the radius of the cylinder and R(t) is the bending radius of the fibers. In this figure, it is seen that all glass fibers were deformed at temperatures below the glass transition temperature, i.e., stress relaxation occurs even below the glass transition temperature. It is also seen that the temperature ranges in which the fibers were deformed increase with increasing glass transition temperature and the bending radius approaches the cylinder's radius as the annealing temperature increases. It is also seen that the slopes of bending radius in each fiber are almost equal. The normalized bending radius, Ro/R(t), is shown as a function of the logarithm of the annealing time in Fig. 5 for SiO 2 glass fiber.
5. Discussion The stress relaxation mechanisms were analyzed by a log-normal distribution model. Using the normalized bending radius changes shown in Fig. 5, the times at which qJ = R o / R = 0.5 were
M. Koide et al. /Journal of Non-Crystalline Solids 177 (1994) 427-431
Table 2 Kinetic parameters, E, ~'o, and distribution parameters, n, in the KWW equation
(+3 kJ n-~ 0.5
SiO z glass fiber Ge-doped SiO 2 glass fiber F-doped SiO 2 glass fiber Fluoride glass fiber
1.9(_+0.1)×10 -1° 1.2( + 0.1) × 10- 7
4.3( _+0.1) × 10-10
4.5( + 0.1) × 10-17
Fig. 5. Normalized bending radius changes in isothermal
anneealing in SiO 2 glass fibers. Lines are drawn as guides for the eye.
determined for each annealing temperature, and these times are regarded as the relaxation times, r m. Eq. (6) can be rewritten as
log( - In( 1 - ~0)) = n l o g ( t / r ) .
Fig. 6 shows plots of l o g ( - l n ( 1 - ~ ) ) versus l o g ( t / r ) for SiO 2 glass fibers in which the calculated 'Tm were used. The distribution parameter, n, was determined by a least-squares fit to Eq. (8). The distribution parameters obtained, n, are listed in Table 2. The value of n of SiO 2 glass fiber is about 0.5. Because the SiO 2 glass fiber consists of a single component, it is considered that the stress relaxation was caused by a reduction of the free volume, i.e., a rearrangement of bond angle and bond length. In Ge- and F-doped
Fig. 6. Plot of Iog(t/r m) versus l o g ( - In(1 - 0 ) for SiO 2 glass fiber.
SiO z fibers, it is thought that there should be more types of atomic movement compared with those in SiO/ fibers. However, the distribution parameters for these doped glass fibers are larger than that of the SiO/ glass fiber, suggesting narrower distributions of relaxation times. The value of n in fluoride glass fibers is considerably smaller than those in other glass fibers. It is known that the chemical bonds in fluoride glasses are much more ionic than those in the oxide glasses . The fluoride glass fiber used in this study is multicomponent and, therefore, the contribution of the atomic movements to the deformation is complex. The smaller value of n = 0.28 means that the distribution of the relaxation time in fluoride glass fibers is much wider than that of oxide glass fibers. In this paper, the relation between the reduction of free volume and the atomic movement for fiber deformation could not be elucidated. However, it may be supposed that the deformations on each of the fibers below the glass transition temperature are caused by different relaxation mechanisms. The relaxation time is plotted against reciprocal of heat treatment temperature in Fig. 7. The temperature dependence of the relaxation time is expressed by the Arrhenius relation. The activation energy, E, for relaxation and the pre-exponential factor, r0, were determined from these straight lines by least squares fits. The kinetic parameters, E and ~'0, obtained for the present fibers are summarized in Table 2. It is seen that the activation energy of SiO z glass fibers is larger than those of other fibers. In the previous study, it was reported that
M. Koide et aL /Journal of Non-Crystalline Solids 177 (1994) 427-431 1.5
atomic movement for stress relaxation are more important in fluoride glass fibers than in oxide glass fibers. Further, the pre-exponential factor of fluoride glass fiber is considerably smaller than those of other oxide glass fibers. It is obvious that the atomic local environment in fluoride glass differs from those in oxide glass.
SiO 2 fiber
1.C E 0.~,
0 I 0.9
I ID ( K-' )
Fig. 7. Temperature dependence of relaxation time, Tm, in Arrhenius plot.
the activation energies for viscous flow of fluoride glasses at the glass transition temperature are about 400-600 kJ/mol [10,11], and those of oxide glasses are also > 400 kJ/mol . Hence, the deformation mechanism in glass fibers below the glass transition temperature should differ greatly from the viscous flow mechanism near the glass transition temperature. Mackenzie obtained the activation energy of contraction in glass fibers . He reported that the activation energy of sudden contraction in the initial stage was about 20 kJ/mol, much smaller than the activation energy determined from deformation of the stress relaxation in this paper. It is considered that the deformation of SiO 2 glass fibers is caused by a reduction of the free volume due to changes of bond angles and length because this glass contains no other components. It is supposed that the deformation in Ge- and F-doped glass fibers may be caused by the migration of doped ions in addition to the free volume reduction, because the activation energies for relaxation time of Geand F-doped SiO 2 glass fibers are smaller than that of SiO2 fiber. This result may indicate that the deformation of stress relaxation is partly due to the atomic movement with low activation energies. This suggests that the contributions of the
It was found that fluoride and oxide glass fibers can be deformed by bending stress below the glass transition temperature. The deformation mechanisms in glass fibers below the glass transition temperature differ from the viscous flow mechanisms around the glass transition region. It is found that the deformation in fluoride and other glass fibers below the glass transition temperature is caused by different relaxation mechanisms. This work was supported by the Furukawa Electric Co. Ltd.
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