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The radiation effects of very heavy ions on the viscosity of a simple glass
217
Journal of Nuclear Materials 165 (1989) 217-221 North-Holland, Amsterdam
THE EDISON EFFEXXS OF VERY HEAVY IONS ON THE VISCOSITY OF A SIMPLE GLASS A. BARBU, M. BIBOLE, R. LE HAZIF,
S. BOUFFARD
* and J.C. RAMILLON
Centre d’Etudes NucltSaires de Saclay, DPpartement de Technologie, Section de Recherches de MPtallurgie Physique, 91191 Gif-sur- Yvette Cedex, France
Received 2 December 1988; accepted 17 February 1989
We have investigated in a very direct way the effect of irradiation with 1.66 GeV argon ions, on the viscosity of the B,,O, glass. Up to a threshold temperature, a very drastic decrease of the viscosity is observed under irradiation. On a large range of temperature a quasi-athermal behavior appears. This effect is discussed in the framework of two models. The fist one is baaed on an analogy with the diffusion in crystals under irradiation and the second takes into account the deformation of a cylinder of matter which becomes very fluid during a very short time along the ion range.
1. Introduction The knowledge of atomic transport properties and rheological properties of glasses under irradiation is very important for the scientific management of the disposal of high level nuclear wastes and for the technology of nuclear reactors. Although Mayer and Leconte [l] reported as soon as 1961 that the creep rate of a silica fiber under fast neutron irradiation at 6O*C is the same as that at 6OO“C not under irradiation. Very rare studies have been performed concerning the effect of irradiation on the viscosity of glasses, and always by indirect means. Primak [2] for instance shows that the stress relaxation of vitreous silica under ion irradiation can be described as a viscoelastic behavior in which the apparent viscosity is reduced to 1019 N/m2 s. Moreover, he observed the same behavior with low energy electron irradiation which does not induce atomic displacements by elastic collisions. Finally, we recently showed, by studying the kinetics of coagulation of lead particles in B203 that the viscosity of this glass is drastically reduced by e- irradiations even at energies under the displacement threshold and that an athermal behavior is observed for 1 MeV e- but not at 125 keV e- j3,4].
* Centre Interdisciplinaire Caen.
de Recherche avec les Ion Lourds,
0022-3115/89/$03.50 0 Elsevier (Noah-Homed Physics abusing
Science Publishers Division)
The purpose of this study was to confirm this very important effect of irradiation by using a direct method on a very simple glass, the creep of B,Os glass fibers.
2. Experimentalprocedure The experiments were performed at the Grand Accelerateur National d’Ions Lourds (GANIL) at Caen. The viscosity was measured by a fiber elongation technique. A special device has been built to be fixed at IRABAT 2, the irradiation device of the CIRIL (Centre Interdisciplinaire de Recherche avec les Ions Lourds). Three parameters are measured during the experience: the flux of particles, the fiber temperature and the creep rate. The particle flux (1.66 GeV argon) is continuously followed by measuring the current induced by the flow of ions through a thin foil of tantalum after calibration by means of the Faraday cup. The flux of particles is modified by changing the irradiated area. Its value is equal to or less than 10” ions cmW2 s-*. The fiber is directly heated by the particle beam. The energy losses by electronic excitation are mainly converted into heat. The fiber is irradiated over 15 mm. Its temperature is changed by modifying the particle flux and the helium pressure in the specimen chamber. For this purpose it is isolated from the accelerator by a thin foil of stainless steel (thickness, 12 pm). B.V.
A. Barbu er al. / Radiation effects of very heavy ions
218
Table 1 Z and 7 as a function of the flux (+), the temperature is
The temperature of the irradiated area is measured through a saphire window by means of a radiometric infrared microscope previously calibrated on a glass fiber heated by a hot air stream. The elongation of the fiber is given by an inductive transducer (LVDT). The B,_O, glass fibers were drawn out from the melt. The diameter of the fibers was near 1 mm, slightly less than the range of Ar 1.66 GeV in B,Os (1.4 mm).
variable
3. Experimental results In view of the highest accessible ion flux and with an atmospheric pressure of helium within the experimental enclosure we have been able to measure the creep velocity of the fiber between 153’C (3.7 X 10” ions cm-’ s-l ) and 326 o C (10” ions cma2 s-l). As expected by theoretical calculations [S], the heating of the fiber varies linearly with the particle flux. Elongation versus time shows a linear behavior as soon as the temperature is stabilized. The time of stabilisation is of the order of some seconds with the atmospheric pressure of helium used in our experiments but much too long under vacuum. At the end of the experiment the total elongation of the fibers is reduced to 1 mm corresponding to a very small relative variation of diameter (3 x 10m2). The stress can then be assumed to be constant during the experiment. The values of the elongation rate < for the set of each flux-temperature (+, T) couple experienced on
Viscosity without irradiation,
+ (cm
153 163 171 183 201 223 258 307 326
3.7XlO’O 4 XlO’O 4.6 x 10” 4.8 x 10” 5.5 x 10’0 6.3 x 10” 7.6 x 10” 9.3 x 10’0 1 x10”
s-l
)
< (s-l)
1) W/m’)
2.5~10-~ 5.2~10-~ 6.7~10-~ 6.5x10K6 1.1 x10-s 1.4x10-5 1.7x10-5 1.7x10-4 4.7x10-4
8.3x10” 4.0x10” 3.1 x 10” 3.2 x 10” 1.9 x 10” 1.5 x 10” 1.2 x 10” 1.2 x 10’0 4.4 x 109
one fiber are reported on table 1. T’he experiment was repeated on a second fiber with the same results. The Newtonian behavior can be characterised by a viscosity coefficient 7 given by: v=---
4 Fl 37 d2 i ’
where i is the strain rate, d the diameter of the fiber and F the applied load.
4. Discussion
The values of q under irradiation and not under irradiation have been plotted on a Arrhenius graph (fig.
10000/T Fig. 1. -
-2
T(“C)
(K-l)
. . . . . . viscosity under irradiation (40Ar 44 MeV/R).
219
A. Barbu et al. / Radiation effects of very heavy ions
1). We observe that the behavior of the viscosity under 1.66 GeV argon ion irradiation is characterized by: - A drastic lowering of q under irradiation. - The existence of an athermal shelf at medium temperature. - A significant increase of viscosity with decreasing temperature at low temperature. Such a behavior is qualitatively the same as those under 1 MeV electron irradiation obtained by the very indirect way previously mentioned [3]. At high temperature irradiation does not affect the viscosity of the glass. This is a well known and a general behavior of macroscopic properties under irradiation. It is worth noticing that the perfect superposition of both curves outside and under irradiation at high temperature is a very good verification of the temperature measurement under the ion beam. It would have been better to obtain the viscosity coefficient at constant ion flux. However most macroscopic properties of solids under irradiation show in the stationary state a @ dependence with n I 1. Fig. 2 shows that corrections to get q at constant flux for n = 1 does not change the main feature of the Arrhenius plot of n; the athermal behavior is simply more obvious. Unfortunately, because of the sensibility limit of our method, it was not possible to study precisely the very significant increase of viscosity at the lower temperatures
10’2
N ‘E
IO”
z” C 10'0
I
1.7
I
1.8
I
1.9 1000/T
I
I
I
2.0
2.1
2.2
I
2.3
(K-l)
viscosity Fig. 2. - - - Viscosity without irradiation, under irradiation (experimentalresults), . . . . . . viscosity under irradiation calculated for constant ions flux (correction made with the assumption that the viscosity is a linear fonction of the flux).
Lo
1/II*
l/T Fig. 3. Inverse of the copper diffusion coefficient calculated for different defect production rates (K) and dislocation densities (p) after [7]. 1: K = 10e6 s-l, p = 10” m-*; 2: K = 10e6 s-l, p=104 m-2; 3: ~=10-6 s-1, p=lOis me2; 4: K=10m4 s-l, p = 10” rnm2.
The origin of the drastic reduction of the viscosity under irradiation is not really understood. However an analogy between the behavior of the viscosity and the atomic diffusion coefficient in crystals under irradiation is well known [4]. It is not very surprising in so far as the viscosity model of glass [6] shows that if the same ‘defect’ is responsible for both viscosity and diffusion, the viscosity coefficient is in inverse proportion to the diffusion coefficient. To illustrate this analogy we have plotted on an Arrhenius diagram the inverse of the self-diffusion coefficient in copper under irradiation, one of the very rare studies of the radiation effect on diffusion [7] (see fig. 3). If the analogy is not fortuitous it must be assumed that the viscosity is controlled by defects created by pairs which are able to disappear either by recombination or by elimination on the sink. The athermal plateau would be associated with a sink elimination regime and the low temperature behavior to a recombination regime. It has recently been shown that the e- irradiation effect is mainly due to electronic energy losses but that the athermal plateau only exists above some atomic displacement threshold [3,4]. The defect sinks would then be produced by atomic displacement only. The nature of these sinks and of the defects are not yet clear; it could be a local modification of the struc-
220
A. Barbu et al. / Radiation effects of very heavy ions
&E
0
1 t
4
Trace
Fig. 4. Events sequence giving a deformation increment of the trace.
ture of the glass for the former and Frenkel
pairs or dangling bonds for the latter. Until now we implicitly assumed that the defects are created homogeneously in the fiber. If it is well founded for electron irradiation it is obviously not true for high energy ions. For this latter case, it is well known that the energy is mainly deposited via electronic energy losses and that it is localized within a radius of some nanometers around the range of the ion. Some atoms are displaced by elastic collisions but this latter kind of energy deposition (nuclear losses) is about a thousand times smaller than the former. Along the range of the impinging ion the rate of energy deposition is about 1O22 eV cme3 SC*. This value is 10’ times higher than those injected in a homogeneous way in the case of electron irradiation such as those we performed in. a high voltage electron microscope. A very drastic lowering of the viscosity in a cylinder of some nanometers in diameter around the range of the ions is then expected for a very short duration 8 of the order of lo-l2 s. Taking this aspect explicitly into account, an alternative and totally different model may be proposed. We can, assuming that the behavior of the glass is elastic outside the traces and viscoelastic inside for a duration 8, calculate the creep velocity of the material. As all the traces are parallel, across all the fibers and as their lateral extensions are very small compared to the dimensions of the fiber, it can be reasonably assumed that we are dealing with a planar system. During a short duration 8, the material within the trace behaves viscoelastically and then becomes again purely elastic like the matrix.
If the trace is very fluid during 8, the trace behaves like a hole, deforms and solidifies again with no stress inside. The result is a permanent increment of deformation 6r (fig. 4). For the sake of simplicity, we assume that the stress concentration in the matrix is quickly relaxed.
E
0 Fig. 5. Rheological model.
A. Barbu et al. / Radiation effects of very heavy ions
If the trace behaves in a viscoelastic way some stresses remain in the trace after solidification and the permanent deformation is smaller than Se. If the behavior of the trace is totally elastic (q very large) there is indeed no more permanent deformation and 6t = 0. Let us assume for the sake of simplicity that the fiber has a square section of side A and that the trace also has a square section of side a. The system during 13 and only during B can be represented by the rheological model schematically shown on fig. 5. The left hand part of this figure depicts the matrix taking into account the stress releases induced by all the old traces. It can be shown that its elastic behavior is the same as that of the origin matrix. The right hand part of this figure depicts the trace. In this figure, (I = F/A and (A-u) u=u,-----+aq, A
a
where F is the load applied to the fiber, The creep velocity of the fiber is then given by the relation g=+(l-ekp(-$))
(1)
with r z q/E, where E is Young’s modulus. If the trace is very fluid during the time B the relation becomes r’= oa*+/E,
221
By taking K, = 1013 cascades crne3 s-i and a = 10 nm we found n = 10 ** N s m-* a value 10 orders of magnitude above the athermal plateau. The nuclear collisions cannot be at the origin of the drop of viscosity of the glass.
5. Conclusion It has been shown by a simple direct method that irradiations with very fast heavy ions drastically reduce the viscosity of the simple B,O, glass. The behavior of the viscosity is very similar to that previously observed by 1 MeV electron irradiation: - no effect at high temperature; - an athermal plateau at intermediate temperature; _ an increase at low temperature. We have shown that despite an interpretation based on the analogy with diffusion under irradiation cannot be avoided, another explanation considering the deformation of transient fluid traces is quite attractive. In the latter case however, the similitude between irradiation effects by electrons and heavy ions would be fortuitous. Specific experiments should be designed to resolve this ambiguity.
(2)
6 no longer depends on the tem~rature
or the lifetime of the trace. It exhibits an athermal behavior. The departure of this athermal behavior observed experimentally could be due to the effect of the term in brackets in eq. (1). Taking E = 4 X 10” N ma2 the value of viscosity at the thermal shelf is found for o = 18.4 nm. This value, although slightly too large, is nevertheless reasonable. A similar simple model can be developed to estimate the effect of nuclear collisions on the viscosity. Assuming that the energy is deposited within displacement cascades, of lateral extension a’, that during a short period of time their volume is highly fluid, the creep rate due to nuclear losses i, is given by c,* = ~I’~KJE, where KC is the rate of cascade creation.
References
111G. Mayer and M. Leconte, J. Phys. Radium 21 (1960) 246. 121W. Primah, J. Appl. Phys. 53 (1982) 7331. 131 I. Biron and A. Barbu, Appl. Phys. Lett. 48 (1986) 24,1645. f41 1. Biron and A. Barbu, International Congress on Radia-
tion Effects in Insulators - 4, 6-10 July 1987, Lyon, Frame. I51 HS. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University Press, 1959). Fl F. Spaepen, in: Physique des Ddfauts Les Houches Lectures XXXV, Eds. R. Balian, M. Kleman and J.P. Pokier (North-Holland, Amsterdam, 1980) pp. 133-172. I71 S.J. Rothman, in: Phase Transformation During Irradiation, Ed. F.V. Nolfi, Jr. (Applied Science Publishers, London, 1983) p. 189-211.
Journal of Nuclear Materials 165 (1989) 217-221 North-Holland, Amsterdam
THE EDISON EFFEXXS OF VERY HEAVY IONS ON THE VISCOSITY OF A SIMPLE GLASS A. BARBU, M. BIBOLE, R. LE HAZIF,
S. BOUFFARD
* and J.C. RAMILLON
Centre d’Etudes NucltSaires de Saclay, DPpartement de Technologie, Section de Recherches de MPtallurgie Physique, 91191 Gif-sur- Yvette Cedex, France
Received 2 December 1988; accepted 17 February 1989
We have investigated in a very direct way the effect of irradiation with 1.66 GeV argon ions, on the viscosity of the B,,O, glass. Up to a threshold temperature, a very drastic decrease of the viscosity is observed under irradiation. On a large range of temperature a quasi-athermal behavior appears. This effect is discussed in the framework of two models. The fist one is baaed on an analogy with the diffusion in crystals under irradiation and the second takes into account the deformation of a cylinder of matter which becomes very fluid during a very short time along the ion range.
1. Introduction The knowledge of atomic transport properties and rheological properties of glasses under irradiation is very important for the scientific management of the disposal of high level nuclear wastes and for the technology of nuclear reactors. Although Mayer and Leconte [l] reported as soon as 1961 that the creep rate of a silica fiber under fast neutron irradiation at 6O*C is the same as that at 6OO“C not under irradiation. Very rare studies have been performed concerning the effect of irradiation on the viscosity of glasses, and always by indirect means. Primak [2] for instance shows that the stress relaxation of vitreous silica under ion irradiation can be described as a viscoelastic behavior in which the apparent viscosity is reduced to 1019 N/m2 s. Moreover, he observed the same behavior with low energy electron irradiation which does not induce atomic displacements by elastic collisions. Finally, we recently showed, by studying the kinetics of coagulation of lead particles in B203 that the viscosity of this glass is drastically reduced by e- irradiations even at energies under the displacement threshold and that an athermal behavior is observed for 1 MeV e- but not at 125 keV e- j3,4].
* Centre Interdisciplinaire Caen.
de Recherche avec les Ion Lourds,
0022-3115/89/$03.50 0 Elsevier (Noah-Homed Physics abusing
Science Publishers Division)
The purpose of this study was to confirm this very important effect of irradiation by using a direct method on a very simple glass, the creep of B,Os glass fibers.
2. Experimentalprocedure The experiments were performed at the Grand Accelerateur National d’Ions Lourds (GANIL) at Caen. The viscosity was measured by a fiber elongation technique. A special device has been built to be fixed at IRABAT 2, the irradiation device of the CIRIL (Centre Interdisciplinaire de Recherche avec les Ions Lourds). Three parameters are measured during the experience: the flux of particles, the fiber temperature and the creep rate. The particle flux (1.66 GeV argon) is continuously followed by measuring the current induced by the flow of ions through a thin foil of tantalum after calibration by means of the Faraday cup. The flux of particles is modified by changing the irradiated area. Its value is equal to or less than 10” ions cmW2 s-*. The fiber is directly heated by the particle beam. The energy losses by electronic excitation are mainly converted into heat. The fiber is irradiated over 15 mm. Its temperature is changed by modifying the particle flux and the helium pressure in the specimen chamber. For this purpose it is isolated from the accelerator by a thin foil of stainless steel (thickness, 12 pm). B.V.
A. Barbu er al. / Radiation effects of very heavy ions
218
Table 1 Z and 7 as a function of the flux (+), the temperature is
The temperature of the irradiated area is measured through a saphire window by means of a radiometric infrared microscope previously calibrated on a glass fiber heated by a hot air stream. The elongation of the fiber is given by an inductive transducer (LVDT). The B,_O, glass fibers were drawn out from the melt. The diameter of the fibers was near 1 mm, slightly less than the range of Ar 1.66 GeV in B,Os (1.4 mm).
variable
3. Experimental results In view of the highest accessible ion flux and with an atmospheric pressure of helium within the experimental enclosure we have been able to measure the creep velocity of the fiber between 153’C (3.7 X 10” ions cm-’ s-l ) and 326 o C (10” ions cma2 s-l). As expected by theoretical calculations [S], the heating of the fiber varies linearly with the particle flux. Elongation versus time shows a linear behavior as soon as the temperature is stabilized. The time of stabilisation is of the order of some seconds with the atmospheric pressure of helium used in our experiments but much too long under vacuum. At the end of the experiment the total elongation of the fibers is reduced to 1 mm corresponding to a very small relative variation of diameter (3 x 10m2). The stress can then be assumed to be constant during the experiment. The values of the elongation rate < for the set of each flux-temperature (+, T) couple experienced on
Viscosity without irradiation,
+ (cm
153 163 171 183 201 223 258 307 326
3.7XlO’O 4 XlO’O 4.6 x 10” 4.8 x 10” 5.5 x 10’0 6.3 x 10” 7.6 x 10” 9.3 x 10’0 1 x10”
s-l
)
< (s-l)
1) W/m’)
2.5~10-~ 5.2~10-~ 6.7~10-~ 6.5x10K6 1.1 x10-s 1.4x10-5 1.7x10-5 1.7x10-4 4.7x10-4
8.3x10” 4.0x10” 3.1 x 10” 3.2 x 10” 1.9 x 10” 1.5 x 10” 1.2 x 10” 1.2 x 10’0 4.4 x 109
one fiber are reported on table 1. T’he experiment was repeated on a second fiber with the same results. The Newtonian behavior can be characterised by a viscosity coefficient 7 given by: v=---
4 Fl 37 d2 i ’
where i is the strain rate, d the diameter of the fiber and F the applied load.
4. Discussion
The values of q under irradiation and not under irradiation have been plotted on a Arrhenius graph (fig.
10000/T Fig. 1. -
-2
T(“C)
(K-l)
. . . . . . viscosity under irradiation (40Ar 44 MeV/R).
219
A. Barbu et al. / Radiation effects of very heavy ions
1). We observe that the behavior of the viscosity under 1.66 GeV argon ion irradiation is characterized by: - A drastic lowering of q under irradiation. - The existence of an athermal shelf at medium temperature. - A significant increase of viscosity with decreasing temperature at low temperature. Such a behavior is qualitatively the same as those under 1 MeV electron irradiation obtained by the very indirect way previously mentioned [3]. At high temperature irradiation does not affect the viscosity of the glass. This is a well known and a general behavior of macroscopic properties under irradiation. It is worth noticing that the perfect superposition of both curves outside and under irradiation at high temperature is a very good verification of the temperature measurement under the ion beam. It would have been better to obtain the viscosity coefficient at constant ion flux. However most macroscopic properties of solids under irradiation show in the stationary state a @ dependence with n I 1. Fig. 2 shows that corrections to get q at constant flux for n = 1 does not change the main feature of the Arrhenius plot of n; the athermal behavior is simply more obvious. Unfortunately, because of the sensibility limit of our method, it was not possible to study precisely the very significant increase of viscosity at the lower temperatures
10’2
N ‘E
IO”
z” C 10'0
I
1.7
I
1.8
I
1.9 1000/T
I
I
I
2.0
2.1
2.2
I
2.3
(K-l)
viscosity Fig. 2. - - - Viscosity without irradiation, under irradiation (experimentalresults), . . . . . . viscosity under irradiation calculated for constant ions flux (correction made with the assumption that the viscosity is a linear fonction of the flux).
Lo
1/II*
l/T Fig. 3. Inverse of the copper diffusion coefficient calculated for different defect production rates (K) and dislocation densities (p) after [7]. 1: K = 10e6 s-l, p = 10” m-*; 2: K = 10e6 s-l, p=104 m-2; 3: ~=10-6 s-1, p=lOis me2; 4: K=10m4 s-l, p = 10” rnm2.
The origin of the drastic reduction of the viscosity under irradiation is not really understood. However an analogy between the behavior of the viscosity and the atomic diffusion coefficient in crystals under irradiation is well known [4]. It is not very surprising in so far as the viscosity model of glass [6] shows that if the same ‘defect’ is responsible for both viscosity and diffusion, the viscosity coefficient is in inverse proportion to the diffusion coefficient. To illustrate this analogy we have plotted on an Arrhenius diagram the inverse of the self-diffusion coefficient in copper under irradiation, one of the very rare studies of the radiation effect on diffusion [7] (see fig. 3). If the analogy is not fortuitous it must be assumed that the viscosity is controlled by defects created by pairs which are able to disappear either by recombination or by elimination on the sink. The athermal plateau would be associated with a sink elimination regime and the low temperature behavior to a recombination regime. It has recently been shown that the e- irradiation effect is mainly due to electronic energy losses but that the athermal plateau only exists above some atomic displacement threshold [3,4]. The defect sinks would then be produced by atomic displacement only. The nature of these sinks and of the defects are not yet clear; it could be a local modification of the struc-
220
A. Barbu et al. / Radiation effects of very heavy ions
&E
0
1 t
4
Trace
Fig. 4. Events sequence giving a deformation increment of the trace.
ture of the glass for the former and Frenkel
pairs or dangling bonds for the latter. Until now we implicitly assumed that the defects are created homogeneously in the fiber. If it is well founded for electron irradiation it is obviously not true for high energy ions. For this latter case, it is well known that the energy is mainly deposited via electronic energy losses and that it is localized within a radius of some nanometers around the range of the ion. Some atoms are displaced by elastic collisions but this latter kind of energy deposition (nuclear losses) is about a thousand times smaller than the former. Along the range of the impinging ion the rate of energy deposition is about 1O22 eV cme3 SC*. This value is 10’ times higher than those injected in a homogeneous way in the case of electron irradiation such as those we performed in. a high voltage electron microscope. A very drastic lowering of the viscosity in a cylinder of some nanometers in diameter around the range of the ions is then expected for a very short duration 8 of the order of lo-l2 s. Taking this aspect explicitly into account, an alternative and totally different model may be proposed. We can, assuming that the behavior of the glass is elastic outside the traces and viscoelastic inside for a duration 8, calculate the creep velocity of the material. As all the traces are parallel, across all the fibers and as their lateral extensions are very small compared to the dimensions of the fiber, it can be reasonably assumed that we are dealing with a planar system. During a short duration 8, the material within the trace behaves viscoelastically and then becomes again purely elastic like the matrix.
If the trace is very fluid during 8, the trace behaves like a hole, deforms and solidifies again with no stress inside. The result is a permanent increment of deformation 6r (fig. 4). For the sake of simplicity, we assume that the stress concentration in the matrix is quickly relaxed.
E
0 Fig. 5. Rheological model.
A. Barbu et al. / Radiation effects of very heavy ions
If the trace behaves in a viscoelastic way some stresses remain in the trace after solidification and the permanent deformation is smaller than Se. If the behavior of the trace is totally elastic (q very large) there is indeed no more permanent deformation and 6t = 0. Let us assume for the sake of simplicity that the fiber has a square section of side A and that the trace also has a square section of side a. The system during 13 and only during B can be represented by the rheological model schematically shown on fig. 5. The left hand part of this figure depicts the matrix taking into account the stress releases induced by all the old traces. It can be shown that its elastic behavior is the same as that of the origin matrix. The right hand part of this figure depicts the trace. In this figure, (I = F/A and (A-u) u=u,-----+aq, A
a
where F is the load applied to the fiber, The creep velocity of the fiber is then given by the relation g=+(l-ekp(-$))
(1)
with r z q/E, where E is Young’s modulus. If the trace is very fluid during the time B the relation becomes r’= oa*+/E,
221
By taking K, = 1013 cascades crne3 s-i and a = 10 nm we found n = 10 ** N s m-* a value 10 orders of magnitude above the athermal plateau. The nuclear collisions cannot be at the origin of the drop of viscosity of the glass.
5. Conclusion It has been shown by a simple direct method that irradiations with very fast heavy ions drastically reduce the viscosity of the simple B,O, glass. The behavior of the viscosity is very similar to that previously observed by 1 MeV electron irradiation: - no effect at high temperature; - an athermal plateau at intermediate temperature; _ an increase at low temperature. We have shown that despite an interpretation based on the analogy with diffusion under irradiation cannot be avoided, another explanation considering the deformation of transient fluid traces is quite attractive. In the latter case however, the similitude between irradiation effects by electrons and heavy ions would be fortuitous. Specific experiments should be designed to resolve this ambiguity.
(2)
6 no longer depends on the tem~rature
or the lifetime of the trace. It exhibits an athermal behavior. The departure of this athermal behavior observed experimentally could be due to the effect of the term in brackets in eq. (1). Taking E = 4 X 10” N ma2 the value of viscosity at the thermal shelf is found for o = 18.4 nm. This value, although slightly too large, is nevertheless reasonable. A similar simple model can be developed to estimate the effect of nuclear collisions on the viscosity. Assuming that the energy is deposited within displacement cascades, of lateral extension a’, that during a short period of time their volume is highly fluid, the creep rate due to nuclear losses i, is given by c,* = ~I’~KJE, where KC is the rate of cascade creation.
References
111G. Mayer and M. Leconte, J. Phys. Radium 21 (1960) 246. 121W. Primah, J. Appl. Phys. 53 (1982) 7331. 131 I. Biron and A. Barbu, Appl. Phys. Lett. 48 (1986) 24,1645. f41 1. Biron and A. Barbu, International Congress on Radia-
tion Effects in Insulators - 4, 6-10 July 1987, Lyon, Frame. I51 HS. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University Press, 1959). Fl F. Spaepen, in: Physique des Ddfauts Les Houches Lectures XXXV, Eds. R. Balian, M. Kleman and J.P. Pokier (North-Holland, Amsterdam, 1980) pp. 133-172. I71 S.J. Rothman, in: Phase Transformation During Irradiation, Ed. F.V. Nolfi, Jr. (Applied Science Publishers, London, 1983) p. 189-211.