- Email: [email protected]
Electronic slowing down-induced dimensional changes in amorphous Fe85B15
Nuclear Instruments
and Methods in Physics
ResearchB 107(1996) 185- 188
Beam Interactions with Materials A Atoms
ELSEVIER
Electronic slowing down-induced dimensional changes in amorphous A. Audouard a**, J. Dural b, M. Toulemonde b, A. bvas L. Thorn6 e
‘, G. Szenes d,
a Laboraroire de Physique des Solides (CNRS-ERS I 11) and SNCMP (CNRS-UMS 819), Complexe Scientifique de Rangueil, 31077 Toulouse, France b ClRIL, rue Claude Bloch, B.P. 5133,14040 Caen Cedex, France ’ Institute for Solid State Physics, KFKI, PG. Box 49, 1525 Budapest, Hungary e Institute for General Physics, EiitoBs Uniuersity, Museum krt 6-8, H-1088 Budapest. Hungary ’ CSNSM, IN2P3-CNRS. Birt 108, B.P. I, 91405 Orsay, France
Abstract
FessB,s amorphous ribbons were irradiated at a temperature of 80 K with GeV Pb ions. In the considered electronic slowing down range ((d E/dx), = 45 keV/nm), both resistivity variation and anisotropic growth are induced. Several samples with different tilt angles to the beam axis were irradiated at the same time which allowed us to derive information on both resistivity and dimensional variations from in situ resistance measurements. It is shown that (i) the growth starts with a non zero rate and (ii) an additional resistance variation occurs at high fluence. The growth features which are at variance with the previously reported behaviour of dimensional variations induced at lower electronic slowing down values are discussed at the light of a recent model. The influence of preirradiation and subsequent annealing on the growth rate is also considered.
It is now established that electronic slowing down (d E/dx), of fast heavy ions induces, besides resistivity increase, anistropic growth in amorphous alloys. Experimental data reported up to now [ 1,2] are in agreement with the following features: the growth starts with a zero rate and remains weak up to the so-called incubation fluence. Resistivity variations mainly occur in this fluence range. At higher fluence, the irradiated sample respectively shrinks in the direction parallel to the ion beam and expands in the perpendicular one without volume change. The rate of this latter phenomenon remains constant up to the highest fluences. Experimental evidences for the above growth features have been provided by direct measurements of sample length after irradiation [l]. However, data are recorded at scarce fluence values and with rather large relative uncertainty below the incubation fluence. In addition, experiments were restricted to (d E/d x), values up to 35 keV/nm (360 MeV Xe ions). As a contrary, in situ electrical resistance data can be recorded throughout irradiation, at high rate. Moreover, both resistivity and dimensional variations can be derived from those measurements, provided that samples with
different tilt angles to the ion beam are irradiated at the same time. However, this method is indirect and it requires drastic assumptions which are detailed hereafter. Let us consider a ribbon tilted by an angle 8 to the beam direction in the plane parallel to both sample thickness (t) and length (L) and restricting ourselves to small deformations. Assuming that dimensional variations are isotropic in the directions perpendicular to the beam we can write: A L/L = A y/y co& + A x/x sin%, A t/t = A y/y sin28 + A x/x CO&~, Aw/w
= A Y/Y,
(1)
where w is the ribbon width, A x/x and A y/y are the relative dimensional variations in the directions parallel and perpendicular to the beam axis, respectively. When the ribbon resistance is measured with current flowing along the sample length, Eqs. (1) yield: AR/R,=R-L(1
-3sin20),
(2)
where R=Ap/po-Av/3v,,
(3)
and * Corresponding
author.
(4)
L=Ax/x-Av/3v,.
0168-583X/%/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00809-8
III. SHI-INDUCED
EFFECTS
186
A. Audouard et.al./Nucl.
Instr. and Meth. in Phys. Res. B 107 (1996) 185-188
AR/R,, Ap/p, and Au/v0 are the relative resistance, resistivity and volume variations respectively. Bqs. (l)-(4) require that dimensional variations are (i) linked to the ion beam only and (ii) isotropic in the directions perpendicular to the beam axis. If we add, as a further assumption, that the sample volume remains constant during irradiation, the usual expression AR/R, = Ap/po - (1-3sin20) A x/x is obtained [2,3] which allows us to discriminate between resistivity and dimensional variations in resistance data. This was found to be in agreement with experimental data recorded for 2.7 GeV Xe irradiation ((d E/dx), = 25 keV/nm) at high fluences [2]. On the opposite side, for the same ion irradiation and in the range far below the incubation fluence (for which Ax/x should vanish) it has been verified that resistance variations are tilt angle-independent, although within a rather large uncertainty, mainly due to a lack of accuracy in the tilt angle values. The whole resistance variations has been satisfactory accounted for by a phenomenological model which assumes a two-hit phenomenon for the growth. This model which is developed in Ref. [2] involves three parameters D,, aC and G, which are the initial resistivity increase rate, the incubation fluence and the steady state growth rate, respectively. It is used to derive two equations which describe respectively the resistivity variation and the growth:
~=Dr&(l-exp(-
Ax,x--G~(~-9[1-exP(-~)]).
$)),
c6)
These equations reproduce the generally admitted features of both resistivity variation (saturating behaviour at high fluence) and growth (zero/constant) rate far below/above the incubation fluence). If no volume change is induced by irradiation D, and G, should have the same values as d R/d@ at zero fluence and -d L/d@ at high fluence, respectively. As stressed above, the growth model has only been checked in the (d E/d xje range up to 35 keV/nm. The aim of this paper is thus to explore the higher (d E/d x), range and to get more information on the influence of the induced defects on the anisotropic growth. To achieve these purposes, 14 pm thick Fe,,B,, amorphous ribbons were irradiated with 5.2 GeV Pb ions (CdE/dx), = 45 keV/nm) at GANIL in the IRABAT facility [4] at 80 K, with different tilt angles to the beam axis (0” 5 8 < 4.5”). Experimental details have been given elsewhere [2]. After irradiation at some given fluences in the constant growth rate regime, 30 min annealings were performed, in the temperature range from 176 to 343 K, afterwards, samples were further irradiated at 80 K. Two sets of samples were irradiated in the same conditions: only annealing temperatures and fluences at which annealings were performed
differ from one irradiation run to the other. Both irradiation runs gave reproducible and consistent data. Fig. 1 displays the influence of the tilt angle on the fluence dependence of the samples resistance. Annealings have been performed at fluences indicated by arrows in the figure. Data of Fig. 1 are plotted in Fig. 2 as a function of sin% for some fluences. As can be observed, a linear variation is obtained in agreement with Eq. (2) which is used to derive R and L variations. The deduced fluence dependencies of R and L are plotted in Fig. 3. Fig. 4 collects the annealing temperature dependence of the recovery of both R and L (Fig. 4a) and of the initial growth rate measured during the subsequent irradiation (Fig. 4b). As expected, the amount of recovery of the resistivity-dependent parameter(R) increases as the annealing temperature increases while that of the sample dimensions-dependent part (L) remains very small, in agreement with Ref. [l]. Nevertheless, the initial growth rate during the subsequent irradiations decreases towards the value measured for virgin samples as the annealing temperature increases. This demonstrates that the initial growth rate depends on the concentration and probably on the configuration of the remaining defects. Let us consider now the analysis of the irradiation data itself. Full lines in Fig. 3 are fits according to Eqs. (5) and (6) to the data in the fluence range below the first annealing (@ 5 2.2 X lOi cm- *> for the fluence dependence of R and L, respectively. Both fits have been obtained with the same set of parameters (D, - 3.2 X lo-i4 cm’, 3 9~ 10” cm-’ and G,= 1.0X lo-l4 cme2). While a good agreement between R data and Eq. (5) can be observed, a non zero initial rate can be seen for L (-(dL/d@),=5X lo-l5 cm*> so that Bq. (6) fails to reproduce the experimental data at low fluences. On the
23? K
5.2 GeV Pb
0
2
4
6
a
fluence (1 012 cm2) Fig. I. Fiuence dependence of the samples resistance. The tilt angle value is indicated in the figure. Annealiags were performed at fluences indicated by the arrows.
A. Audouard
ei.al./Nucl.
Insw.
and Meth.
in Phys.
Res.
B 107 (1996)
0.016
185-188
187
(4
d
CT w 0.02
0.012
-
0.008
-
0.004
I
. .
.
%
a
. .
1
0.01
0.00
I
’
0.2
0.0
0.4
0.6
sin*(e)
Fig. 2. Tilt angle (0) dependence of the samples resistance recorded at fluence values indicated in the figure. Data are deduced from Fig. I. Straight lines are fits to Eq. (2) (see text). -50
side, a non zero R rate is observed at high fluence ((dR/d@), = 2.5 X lO_” cm2, according to the straight line in Fig. 3. The above non zero rates could be both considered as the signature of a volume change. Assuming that (i) the growth model holds and (ii) the rate of the volume change remain fluence-independent yields (see Bqs. (31~(6)) -(dL/d@i), = (dR/d@), which is definitely not in agreement with experimental data. Furthermore, the mass density increase at the end of irradiation (@- 6.5 x 10” cme2 would reach 5% (and would obviously reach an even larger value for higher fluence since (dR/d@), does not exhibit any tendency to saturaopposite
5.2 GeV Pb
-I
0
2
4
6
8
fluence (1 O’*cm~*)
Fig. 3. Fluence dependence of R (black symbols) and L (open symbols) deduced from Fig. 2. Full lines are tits to the data according to Eqs. (5) and (6) (see text).
150
250
350
annealing temperature (KJ Fig. 4. Annealing temperature dependence of R (black symbols) and L (open symbols) (a) and of the normal&d initial growth rate recorded during subsequent irradiation (b). Squares and circles stand for two sample sets, respectively.
tion). Such a densification is nonsensical since the amount of free volume or irradiation-induced defects in amorphous alloys cannot be higher than about 2% [51. It must be kept in mind that the phenomenologicai model from which Eqs. (5) and (6) are derived assumes a two-hit phenomenon which thus allows for an incubation fluence QC. However, such model may not hold for high electronic slowing-down. Indeed, in recent calculations based on shear stress relaxation within electronic excitation-induced thermal spikes [6], Trinkaus and Ryazanov have predicted that incubation fluence would only be required at low (dE/dx), and should disappear at sufficiently high (dE/dx),. Indeed, GC has been shown to strongly decrease as (d E/dx), increases [2]. Thus, a non zero initial growth rate could arise in the high electronic slowing-down range. What remains to be explained is then the non zero R rate at high fluence. In a recent experiment [7], swift Xe ion irradiation has been shown to induce important surface modifications in amorphous Fe,Ni,B,, alloy. Such surface modifications which strongly depend on the tilt angle might, in our case, alter the ribbon shape and thus modify the measured resistance. However, the above phenomenon has only been observed on thick samples with a beam spot area less than the film surface area. Under such experimental conditions, the stress relaxation can only occur via a limited region of the free surface which certainly strongly amplifies the observed effects. Moreover, very large fluences are reIII. SHI-INDUCEDEFFECTS
188
A. Audowrd
et.al./Nucl.
Instr. and Meth. in Phys. Res. B IO7 (1996) 185-188
quired (above lOI ions cm - *) for the surface modifications to become significant. Another phenomenon to be considered would be surface sputtering. However unrealistically large sputtering rate (S = 106) could only account for the measured value of (d R/d@),. Finally, non zero off diagonal terms of the deformation tensor could be responsible for the observed effects at high fluence [3,7]. However, the measured L variation remains of the order of only few percent, even at high fluences (see Fig. 3) which certainly reduces the influence of such an artifact. In conclusion, the reported data demonstrate that in the considered high electronic slowing down range, the growth starts with a non zero rate. This feature which is at variance with previously reported behaviour at lower electronic slowing down is in agreement with a recent model [6]. On the high fluence side, an additional contribution to the resistance variation have been evidenced. This contri-
bution whose origin remains puzzling yet occurs at a constant rate. References
PI Ming-dong Hou, S. Klaumiinzer and G. Schumacher, Phys. Rev. B 41 (1990) 1144.
El A. Audouard, E. Balanzat, JC Jousset, D. Lesueur and L. Thorn& J. Phys. Condens. Matter 5 (1993) 995. [31 S. Klaumiinzer and A. Benyagoub, Phys. Rev. B 43 (1991)
7502. [41S. Bouffard, J. Dural, F. Levesque and J.M. Ramillon, Ann.
Phys. (Paris) 4 (1989) 395.
151A. Audouard, J. Balogh, J. DuraJ and J.C. Jousset, Radiat. Eff. 62 (1982) 161; J. Non-Cryst. Solids 50 (1982) 71.
k51H. Trinkaus and A.I. Ryazanov, Phys. Rev. Lett. 74 (1995) 5072. [71A. Gutzmann, S.Klaumiinzer and P. Meier, Phys. Rev. Lett.
74 ( 1995) 2256.
and Methods in Physics
ResearchB 107(1996) 185- 188
Beam Interactions with Materials A Atoms
ELSEVIER
Electronic slowing down-induced dimensional changes in amorphous A. Audouard a**, J. Dural b, M. Toulemonde b, A. bvas L. Thorn6 e
‘, G. Szenes d,
a Laboraroire de Physique des Solides (CNRS-ERS I 11) and SNCMP (CNRS-UMS 819), Complexe Scientifique de Rangueil, 31077 Toulouse, France b ClRIL, rue Claude Bloch, B.P. 5133,14040 Caen Cedex, France ’ Institute for Solid State Physics, KFKI, PG. Box 49, 1525 Budapest, Hungary e Institute for General Physics, EiitoBs Uniuersity, Museum krt 6-8, H-1088 Budapest. Hungary ’ CSNSM, IN2P3-CNRS. Birt 108, B.P. I, 91405 Orsay, France
Abstract
FessB,s amorphous ribbons were irradiated at a temperature of 80 K with GeV Pb ions. In the considered electronic slowing down range ((d E/dx), = 45 keV/nm), both resistivity variation and anisotropic growth are induced. Several samples with different tilt angles to the beam axis were irradiated at the same time which allowed us to derive information on both resistivity and dimensional variations from in situ resistance measurements. It is shown that (i) the growth starts with a non zero rate and (ii) an additional resistance variation occurs at high fluence. The growth features which are at variance with the previously reported behaviour of dimensional variations induced at lower electronic slowing down values are discussed at the light of a recent model. The influence of preirradiation and subsequent annealing on the growth rate is also considered.
It is now established that electronic slowing down (d E/dx), of fast heavy ions induces, besides resistivity increase, anistropic growth in amorphous alloys. Experimental data reported up to now [ 1,2] are in agreement with the following features: the growth starts with a zero rate and remains weak up to the so-called incubation fluence. Resistivity variations mainly occur in this fluence range. At higher fluence, the irradiated sample respectively shrinks in the direction parallel to the ion beam and expands in the perpendicular one without volume change. The rate of this latter phenomenon remains constant up to the highest fluences. Experimental evidences for the above growth features have been provided by direct measurements of sample length after irradiation [l]. However, data are recorded at scarce fluence values and with rather large relative uncertainty below the incubation fluence. In addition, experiments were restricted to (d E/d x), values up to 35 keV/nm (360 MeV Xe ions). As a contrary, in situ electrical resistance data can be recorded throughout irradiation, at high rate. Moreover, both resistivity and dimensional variations can be derived from those measurements, provided that samples with
different tilt angles to the ion beam are irradiated at the same time. However, this method is indirect and it requires drastic assumptions which are detailed hereafter. Let us consider a ribbon tilted by an angle 8 to the beam direction in the plane parallel to both sample thickness (t) and length (L) and restricting ourselves to small deformations. Assuming that dimensional variations are isotropic in the directions perpendicular to the beam we can write: A L/L = A y/y co& + A x/x sin%, A t/t = A y/y sin28 + A x/x CO&~, Aw/w
= A Y/Y,
(1)
where w is the ribbon width, A x/x and A y/y are the relative dimensional variations in the directions parallel and perpendicular to the beam axis, respectively. When the ribbon resistance is measured with current flowing along the sample length, Eqs. (1) yield: AR/R,=R-L(1
-3sin20),
(2)
where R=Ap/po-Av/3v,,
(3)
and * Corresponding
author.
(4)
L=Ax/x-Av/3v,.
0168-583X/%/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00809-8
III. SHI-INDUCED
EFFECTS
186
A. Audouard et.al./Nucl.
Instr. and Meth. in Phys. Res. B 107 (1996) 185-188
AR/R,, Ap/p, and Au/v0 are the relative resistance, resistivity and volume variations respectively. Bqs. (l)-(4) require that dimensional variations are (i) linked to the ion beam only and (ii) isotropic in the directions perpendicular to the beam axis. If we add, as a further assumption, that the sample volume remains constant during irradiation, the usual expression AR/R, = Ap/po - (1-3sin20) A x/x is obtained [2,3] which allows us to discriminate between resistivity and dimensional variations in resistance data. This was found to be in agreement with experimental data recorded for 2.7 GeV Xe irradiation ((d E/dx), = 25 keV/nm) at high fluences [2]. On the opposite side, for the same ion irradiation and in the range far below the incubation fluence (for which Ax/x should vanish) it has been verified that resistance variations are tilt angle-independent, although within a rather large uncertainty, mainly due to a lack of accuracy in the tilt angle values. The whole resistance variations has been satisfactory accounted for by a phenomenological model which assumes a two-hit phenomenon for the growth. This model which is developed in Ref. [2] involves three parameters D,, aC and G, which are the initial resistivity increase rate, the incubation fluence and the steady state growth rate, respectively. It is used to derive two equations which describe respectively the resistivity variation and the growth:
~=Dr&(l-exp(-
Ax,x--G~(~-9[1-exP(-~)]).
$)),
c6)
These equations reproduce the generally admitted features of both resistivity variation (saturating behaviour at high fluence) and growth (zero/constant) rate far below/above the incubation fluence). If no volume change is induced by irradiation D, and G, should have the same values as d R/d@ at zero fluence and -d L/d@ at high fluence, respectively. As stressed above, the growth model has only been checked in the (d E/d xje range up to 35 keV/nm. The aim of this paper is thus to explore the higher (d E/d x), range and to get more information on the influence of the induced defects on the anisotropic growth. To achieve these purposes, 14 pm thick Fe,,B,, amorphous ribbons were irradiated with 5.2 GeV Pb ions (CdE/dx), = 45 keV/nm) at GANIL in the IRABAT facility [4] at 80 K, with different tilt angles to the beam axis (0” 5 8 < 4.5”). Experimental details have been given elsewhere [2]. After irradiation at some given fluences in the constant growth rate regime, 30 min annealings were performed, in the temperature range from 176 to 343 K, afterwards, samples were further irradiated at 80 K. Two sets of samples were irradiated in the same conditions: only annealing temperatures and fluences at which annealings were performed
differ from one irradiation run to the other. Both irradiation runs gave reproducible and consistent data. Fig. 1 displays the influence of the tilt angle on the fluence dependence of the samples resistance. Annealings have been performed at fluences indicated by arrows in the figure. Data of Fig. 1 are plotted in Fig. 2 as a function of sin% for some fluences. As can be observed, a linear variation is obtained in agreement with Eq. (2) which is used to derive R and L variations. The deduced fluence dependencies of R and L are plotted in Fig. 3. Fig. 4 collects the annealing temperature dependence of the recovery of both R and L (Fig. 4a) and of the initial growth rate measured during the subsequent irradiation (Fig. 4b). As expected, the amount of recovery of the resistivity-dependent parameter(R) increases as the annealing temperature increases while that of the sample dimensions-dependent part (L) remains very small, in agreement with Ref. [l]. Nevertheless, the initial growth rate during the subsequent irradiations decreases towards the value measured for virgin samples as the annealing temperature increases. This demonstrates that the initial growth rate depends on the concentration and probably on the configuration of the remaining defects. Let us consider now the analysis of the irradiation data itself. Full lines in Fig. 3 are fits according to Eqs. (5) and (6) to the data in the fluence range below the first annealing (@ 5 2.2 X lOi cm- *> for the fluence dependence of R and L, respectively. Both fits have been obtained with the same set of parameters (D, - 3.2 X lo-i4 cm’, 3 9~ 10” cm-’ and G,= 1.0X lo-l4 cme2). While a good agreement between R data and Eq. (5) can be observed, a non zero initial rate can be seen for L (-(dL/d@),=5X lo-l5 cm*> so that Bq. (6) fails to reproduce the experimental data at low fluences. On the
23? K
5.2 GeV Pb
0
2
4
6
a
fluence (1 012 cm2) Fig. I. Fiuence dependence of the samples resistance. The tilt angle value is indicated in the figure. Annealiags were performed at fluences indicated by the arrows.
A. Audouard
ei.al./Nucl.
Insw.
and Meth.
in Phys.
Res.
B 107 (1996)
0.016
185-188
187
(4
d
CT w 0.02
0.012
-
0.008
-
0.004
I
. .
.
%
a
. .
1
0.01
0.00
I
’
0.2
0.0
0.4
0.6
sin*(e)
Fig. 2. Tilt angle (0) dependence of the samples resistance recorded at fluence values indicated in the figure. Data are deduced from Fig. I. Straight lines are fits to Eq. (2) (see text). -50
side, a non zero R rate is observed at high fluence ((dR/d@), = 2.5 X lO_” cm2, according to the straight line in Fig. 3. The above non zero rates could be both considered as the signature of a volume change. Assuming that (i) the growth model holds and (ii) the rate of the volume change remain fluence-independent yields (see Bqs. (31~(6)) -(dL/d@i), = (dR/d@), which is definitely not in agreement with experimental data. Furthermore, the mass density increase at the end of irradiation (@- 6.5 x 10” cme2 would reach 5% (and would obviously reach an even larger value for higher fluence since (dR/d@), does not exhibit any tendency to saturaopposite
5.2 GeV Pb
-I
0
2
4
6
8
fluence (1 O’*cm~*)
Fig. 3. Fluence dependence of R (black symbols) and L (open symbols) deduced from Fig. 2. Full lines are tits to the data according to Eqs. (5) and (6) (see text).
150
250
350
annealing temperature (KJ Fig. 4. Annealing temperature dependence of R (black symbols) and L (open symbols) (a) and of the normal&d initial growth rate recorded during subsequent irradiation (b). Squares and circles stand for two sample sets, respectively.
tion). Such a densification is nonsensical since the amount of free volume or irradiation-induced defects in amorphous alloys cannot be higher than about 2% [51. It must be kept in mind that the phenomenologicai model from which Eqs. (5) and (6) are derived assumes a two-hit phenomenon which thus allows for an incubation fluence QC. However, such model may not hold for high electronic slowing-down. Indeed, in recent calculations based on shear stress relaxation within electronic excitation-induced thermal spikes [6], Trinkaus and Ryazanov have predicted that incubation fluence would only be required at low (dE/dx), and should disappear at sufficiently high (dE/dx),. Indeed, GC has been shown to strongly decrease as (d E/dx), increases [2]. Thus, a non zero initial growth rate could arise in the high electronic slowing-down range. What remains to be explained is then the non zero R rate at high fluence. In a recent experiment [7], swift Xe ion irradiation has been shown to induce important surface modifications in amorphous Fe,Ni,B,, alloy. Such surface modifications which strongly depend on the tilt angle might, in our case, alter the ribbon shape and thus modify the measured resistance. However, the above phenomenon has only been observed on thick samples with a beam spot area less than the film surface area. Under such experimental conditions, the stress relaxation can only occur via a limited region of the free surface which certainly strongly amplifies the observed effects. Moreover, very large fluences are reIII. SHI-INDUCEDEFFECTS
188
A. Audowrd
et.al./Nucl.
Instr. and Meth. in Phys. Res. B IO7 (1996) 185-188
quired (above lOI ions cm - *) for the surface modifications to become significant. Another phenomenon to be considered would be surface sputtering. However unrealistically large sputtering rate (S = 106) could only account for the measured value of (d R/d@),. Finally, non zero off diagonal terms of the deformation tensor could be responsible for the observed effects at high fluence [3,7]. However, the measured L variation remains of the order of only few percent, even at high fluences (see Fig. 3) which certainly reduces the influence of such an artifact. In conclusion, the reported data demonstrate that in the considered high electronic slowing down range, the growth starts with a non zero rate. This feature which is at variance with previously reported behaviour at lower electronic slowing down is in agreement with a recent model [6]. On the high fluence side, an additional contribution to the resistance variation have been evidenced. This contri-
bution whose origin remains puzzling yet occurs at a constant rate. References
PI Ming-dong Hou, S. Klaumiinzer and G. Schumacher, Phys. Rev. B 41 (1990) 1144.
El A. Audouard, E. Balanzat, JC Jousset, D. Lesueur and L. Thorn& J. Phys. Condens. Matter 5 (1993) 995. [31 S. Klaumiinzer and A. Benyagoub, Phys. Rev. B 43 (1991)
7502. [41S. Bouffard, J. Dural, F. Levesque and J.M. Ramillon, Ann.
Phys. (Paris) 4 (1989) 395.
151A. Audouard, J. Balogh, J. DuraJ and J.C. Jousset, Radiat. Eff. 62 (1982) 161; J. Non-Cryst. Solids 50 (1982) 71.
k51H. Trinkaus and A.I. Ryazanov, Phys. Rev. Lett. 74 (1995) 5072. [71A. Gutzmann, S.Klaumiinzer and P. Meier, Phys. Rev. Lett.
74 ( 1995) 2256.