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Internal friction due to mobile ions in (AgI)x(Ag2O 2B2O3)1−x superionic glasses
Journal of Non-Crystalline Solids 56 (1983) 393-398 North.Holland Publishing Company
393
INTERNAL FRICTION DUE TO MOBILE IONS IN (Agl)x(Ag20 - 2B203)I_ x SUPERIONIC GLASSES G. C a r i n i , M. Curtoni, M. Federico, G. G a l l i and G. Tripodo I n s t i t u t o di Fisica Generale and Gruppo Nazionale di S t r u t t u r a d e l l a Materia del CNR- Messina, I t a l y
The behavior of acoustic a t t e n u a t i o n in (Agl)x(Ag20.2B203)l_ x, where the molar f r a c t i o n x varies from 0 to 0.6, was measured in the temperature range 80 to 470K and at u l t r a s o n i c frequencies (5 to 45 Mhz). The presence of a broad peak, whose p o s i t i o n s h i f t s to higher temperatures with increasing frequency and whose height increases with Agl c o n c e n t r a t i o n , indicates the existence of t h e r m a l l y a c t i v a t e d r e l a x a t i o n processes due to mobile Ag÷ ions. A q u a n t i t a t i v e analysis in terms of a r e l a x a t i o n time d i s t r i b u t i o n , coming from a Gaussian-like d i s t r i b u t i o n function f o r the a c t i v a t i o n energies E, gave a good f i t of the experimental data. All the r e s u l t s are discussed in connection with the possible microscopic s t r u c t u r e o f those glasses. INTRODUCTION Recently anomalies in the acoustic behavior of s i l v e r - h a l i d e - s i l v e r borate glasses nave been a t t r i b u t e d to low temperature t u n n e l l i n g motion (1) and high temperature t h e r m a l l y a c t i v a t e d jumps (2) of Ag+ ions, mobile between d i f f e r e n t p o s i t i o n s in the glassy m a t r i x . Previous work had reached the conclusion t h a t only the presence of very mobile Ag+ ions could explain the low temperature t u n n e l l i n g . On t h i s basis, i t was assumed t h a t the i n t r o d u c t i o n of Agl made i t easy by modifying the glassy network. The measurements in (Agl)x(Ag20 - 2B203)l-x presented in t h i s paper seem to confirm f u r t h e r t h a t hypothesis. Moreover analysis of the experimental data reveals a close connection with the c o n d u c t i v i t y data (3) and allows us to obtain good i n f o r m a t i o n on the behavior of the microscopic s t r u c t u r e o f these glasses with increasing Agl concentration. EXPERIMENTAL PROCEDURE AND RESULTS The (Agl)x(Ag20 - 2B203)l_x glasses were prepared according to the procedure p r e v i o u s l y described (3, 4~. X-ray d i f f r a c t i o n confirmed t h e i r amorphous nature. The absorption and v e l o c i t y of l o n g i t u d i n a l sound waves in the 5 to 45 Mhz and 80 to 470 k ranges were measured using the same apparatus described in r e f . ( l , 2). An epoxy resin was used to o b t a i n a good match between quartz transducers and the samples at temperatures as high as 470k. All the data have been corrected f o r a mean d i f f r a c t i o n loss of ~/a , 'la" being the transducer radius and "~" the ultrasound wavelength in the samples. Figure l shows the temperature behavior of acoustic a t t e n u a t i o n of 5 Mhz l o n g i t u d i n a l sound waves at various x. A broad peak is present in a l l the curves which show increases in height and s h i f t s to lower temperature with increasing Agl content. Moreover, the peak always s h i f t s to higher temperatures with increasing frequency which is t y p i c a l of t h e r m a l l y a c t i v a t e d r e l a x a t i o n s , see Figure 2. 0022-3093/83/0000-0000/$03.00 © 1983 North-Holland
G. Carini et al. /Internal friction due to mobile ions
394
Unfortunately, we were unable to see the peak at frequencies above 15 Mhz because of i t s high temperature (in the binary glass) and i t s very high attenuation (at high concentrations of Agl). However, i t can be seen from the experimental points in Fig. 2 that the peak also exists at higher frequencies. In Figure 3, is shown as a function of ultrasound frequencies as a logarithmic p l o t , having substracted a nearly temperature independent background. This reveals an f2 and fO,9 dependence, respectively on the r i g h t and l e f t hand side of the peak. The other glasses investigated show the same behavior. The 5 Mhz sound v e l o c i t y data, at room temperature, are inserted in Table I. They indicate that the introduction of Agl in Ag202B203 produces a less r i g i d structure in agreement with the corresponding decrease of TG (3). DISCUSSION From the peak temperature s h i f t with frequency, i t was possible to e x t r a c t the frequency factor ~ i and the apparent a c t i v a t i o n energies of the process, according to the r e l a t i o n s (5):
(I)
• X=O.O
,',
0.2
o
0.4
•
0.6
o =
o <:c
100
200
I
I
300
400
I,K Figure I .
Temperature dependence of acoustic attenuation in (Agl)x(Ag20.2B203)l_ x glasses.
G. Carini e t aL
/
In ternal friction due to mobile ions
395
derived from the Arrhenius equation. ~-i =
~le-E/kT
In eq. ( I ) and (2) T is the r e l a x a t i o n and TD2 is the peak temperature at the r e s p e c t i v e l y . The obtained values are maximum r e l a x a t i o n loss value Q~ak at r e l a t i o n between the i n t e r n a l f r i c t i o n temperature independent background has
(2)
time, k the Boltzmann constant, and Tpl ultrasound frequency of ~I or ~2, inserted in Table I together with the 5 Mhz t h a t was derived by the well-known and acoustic absorption (2). A nearly been subtracted.
The f o l l o w i n g remarks can be made: I . The a c t i v a t i o n energies decrease with Agl content and are very s i m i l a r to those obtained from d.c. c o n d u c t i v i t y measurements (3) in the same glasses. This shows t h a t the jumps of s i l v e r ions in the i n t e r s t i c e s of the network are r e a l l y the cause of the observed losses. 2. The disappearance of the peak observed in the b i n a r y glass, also in the form of a shoulder, in the high temperature t a i l of the peaks c h a r a c t e r i z i n g the A g l - r i c h glasses, indicates a decrease of the a c t i v a t i o n energy of i t s r e l a x i n g species due to the a d d i t i o n of Agl. This could agree with a recent hypothesis on i o n i c motion in these glasses (3). On the other hand, the sharp slope change shown from r e l a x a t i o n loss behavior, f o r x ~ 2 is not d i r e c t l y d i s c e r n i b l e on t h a t basis, Figure 4. At l e a s t q u a l i t a t i v e l y , i t is our opinion t h a t a s i m i l a r behavior is to be connected to some kind of a gradual s t r u c t u r a l modif i c a t i o n of the network induced by Agl. To analyze the peak q u a n t i t a t i v e l y , we have taken i n t o account the a t t e n u a t i o n due to a r e l a x i n g process with a s i n g l e r e l a x a t i o n time (5): O 0•
X=0.1
~---15 I
E
•
.£3 0•0 C 0
= io 3S,M
"
,
6~
•.6-,
•
• " •
25P1"~ •
-
• • •
15MhoZ• . 0 0
•
•
" 00 •
• 0•O
•
Oo
, 100
t
I 300
200
I
1
1,00
T, K Figure 2.
Acoustic a t t e n u a t i o n vs. temperature at various frequencies in the x = O.I glass. Note the temperature s h i f t of the peak.
396
G. Carini et al. / Internal friction due to mobile ions
--
D 2"V
~ 1 + ~2~2
(3)
being the r e l a x a t i o n time defined by eq. (2), v is the sound v e l o c i t y and D the r e l a x a t i o n strength. Using the data of Table I , we have obtained the curve represented by the dashed l i n e in Figure 5 f o r the x = 0.6 sample. The wider breadth of the experimental curve shows the existence of a r e l a x a t i o n time d i s t r i b u t i o n , confirming the r e s u l t found in s i m i l a r glasses. In order to account f o r t h i s , we assume t h a t the r e l a x a t i o n processes are associated with the ion jumps in double p o t e n t i a l wells of various b a r r i e r heights E. We also assume t h a t the d i s t r i b u t i o n arises from a d i s t r i b u t i o n of P(E) in the a c t i v a t i o n energy and a single value f o r To . In t h i s respect, the number of wells with a given b a r r i e r height E is p r o p o r t i o n a l to P(E) expressed from: _ I P(E} -(~-}1/2" ~ ' o ' e x p { - ( - ~ o E )2}
(4)
where Em and Eo are connected to the most probable value and to the width o f the d i s t r i b u t i o n , r e s p e c t i v e l y , Eq. (3) f o r the a t t e n u a t i o n is now modified in the f o l l o w i n g form (6). oo
a -- ~
B2 . I
-G
i NP(E)
OJ2~(E) dE
1+~2~2(E)
(5)
where N is the t o t a l number of jumping p a r t i c l e s per u n i t volume, B the deformation p o t e n t i a l , Q the d e n s i t y , v the ultrasound v e l o c i t y and x is given by eq. (2). The best f i t of 5 Mhz in x = 0.6 using eq. (5) is represented bx a continuous l i n e in Figure 5 and i t allowed us to determine Em, Eo, r o and NBc.
X=0.6 10
%
xl0 -3
/
. T= 370K / • T= 143 K ~
2O .21=
10
13
_ f.9
5
15 25
frequency, Mhz Figure 3. Logarithmic p l o t o f vs. frequency on the r i g h t and l e f t hand side of the peak.
I I I .2 .4 .6 Ag I content(mol.ar fraction) Figure 4: Maximum r e l a x a t i o n loss QZ~.~s a function o f Agl concentraton. The c ~ n uous l i n e is only i n d i c a t i v e o f the loss behavior in the x > 2 regions.
G. Carini et al. /Internal friction due to mobile ions
397
TABLE I Values of the apparent a c t i v a t i o n eDergy E, frequency f a c t o r , maximum r e l a x a t i o n loss QD~ak and 5 Mhz sound T O- i v e l o c i t y in (Agl)x(Ag20.2B203)l_ x glasses. molar fraction
E (eV mo1-1 )
$o-1
(sec -1}
0 -1 • 10 3 peak
v I (m/sec)
0.0
0.56
4 . 2 2 x 1014
6.35
4.33 x 10 3
0.1
0.51
3.35
6.77
4 11
0.2
0.48
2.75
8.58
3.97
0.4
0.41
2.65
15.6
3.54
0.6
0.33
2.55
20.6
2.98
Em = 0.31 eV/mol, Eo = 0.07 eV/mol, T~ I = lO14s -I and NB2 = 1.54 .1021 eV2/cm 3. This set of values was successively used to c a l c u l a t e (always by eq. 5) m at 15 Mhz, see the continuous l i n e in Figure 5. In t h i s case, the f i t between the t h e o r e t i c a l curve and experimental points is very good. The close s i m i l a r i t y o f Em (and also x - i ) with the corresponding values of Table I seems to i n d i c a t e t h a t the r e l ~ x a t i o n parameters, as e m p i r i c a l l y deduced,
E30 6
¢o
f-
N U
m o <
~_~1//// • _~__~ I 100
\\~%~_ ~-~_ I 300
-~15Mhz 5Mhz I I 500
T,K Figure 5.
Comparison between the experimental data ( s o l i d c i r c l e s ) and theoretical fit: - - - s i n g l e r e l a x a t i o n time, - - gaussian-like d i s t r i b u t i o n of a c t i v a t i o n energies (see t e x t ) .
398
G. Carini et al.
/ Internal friction due to mobile ions
can be assumed as the most probable values o f the d i s t r i b u t i o n ; however a more extensive analysis is necessary to confirm t h i s p o i n t . F i n a l l y , from the product NB2 we t r i e d to c a l c u l a t e the deformation p o t e n t i a l B assumiming t h a t , being in the presence of a r e l a t i v e l y large E d i s t r i b u t i o n , a l l the Ag+ ions present in the glass can c o n t r i b u t e to the r e l a x a t i o n loss. Using the Ag+ concentration (N - 1.4 . 1022cm-3) we obtain B = 0.33 eV, a value close to t h a t commonly observed in superionic (7) glasses. In conclusion we remark t h a t the existence of unusual losses in s i l v e r h a l i d e - s i l v e r borate glasses is to be connected with the t h e r m a l l y a c t i v a t e d jumps of Ag+ ions in the glassy m a t r i x . A q u a n t i t a t i v e analysis of acoustic a t t e n u a t i o n by a r e l a x a t i o n time d i s t r i b u t i o n allows us to deduce a set of parameters t h a t are reasonable w i t h the microscopic arrangement o f the ions. REFERENCES I. 2. 3. 4. 5. 6. 7.
G. C a r i n i , M. Cutroni, M. Federico, G. G a l l i , G. Tripodo and A. Avogadro, Physica B + C 107 (1981) 175. G. C a r i n i , M. Cutroni, M. Federico and G. G a l l i , Solid State Comm. 44 (1982) 1427. G. C h i o d e l l i , A. M a g i s t r i s , M. V i l l a and J. Bjorkstam, J. Non-Cryst. Solids, 51 (1982) 143. The authors are indebted to G. C h i o d e l l i and A. Magistris who have k i n d l y furnished the superionic glasses. A. S. Nowich and B. S. Berry, Anelastic Relaxation in C r y s t a l l i n e Solids, (Acad. Press, New York 1972) p. 57. S. Hunklinger and W. Arnold, in Physical Acoustics ed. by W. P. Mason and R. N. Thurston, (Academic Press, New York, 1976) p. 155. J. Y. Prieur and D. C i p l y s , Physics B + C 107 (1981) 181.
393
INTERNAL FRICTION DUE TO MOBILE IONS IN (Agl)x(Ag20 - 2B203)I_ x SUPERIONIC GLASSES G. C a r i n i , M. Curtoni, M. Federico, G. G a l l i and G. Tripodo I n s t i t u t o di Fisica Generale and Gruppo Nazionale di S t r u t t u r a d e l l a Materia del CNR- Messina, I t a l y
The behavior of acoustic a t t e n u a t i o n in (Agl)x(Ag20.2B203)l_ x, where the molar f r a c t i o n x varies from 0 to 0.6, was measured in the temperature range 80 to 470K and at u l t r a s o n i c frequencies (5 to 45 Mhz). The presence of a broad peak, whose p o s i t i o n s h i f t s to higher temperatures with increasing frequency and whose height increases with Agl c o n c e n t r a t i o n , indicates the existence of t h e r m a l l y a c t i v a t e d r e l a x a t i o n processes due to mobile Ag÷ ions. A q u a n t i t a t i v e analysis in terms of a r e l a x a t i o n time d i s t r i b u t i o n , coming from a Gaussian-like d i s t r i b u t i o n function f o r the a c t i v a t i o n energies E, gave a good f i t of the experimental data. All the r e s u l t s are discussed in connection with the possible microscopic s t r u c t u r e o f those glasses. INTRODUCTION Recently anomalies in the acoustic behavior of s i l v e r - h a l i d e - s i l v e r borate glasses nave been a t t r i b u t e d to low temperature t u n n e l l i n g motion (1) and high temperature t h e r m a l l y a c t i v a t e d jumps (2) of Ag+ ions, mobile between d i f f e r e n t p o s i t i o n s in the glassy m a t r i x . Previous work had reached the conclusion t h a t only the presence of very mobile Ag+ ions could explain the low temperature t u n n e l l i n g . On t h i s basis, i t was assumed t h a t the i n t r o d u c t i o n of Agl made i t easy by modifying the glassy network. The measurements in (Agl)x(Ag20 - 2B203)l-x presented in t h i s paper seem to confirm f u r t h e r t h a t hypothesis. Moreover analysis of the experimental data reveals a close connection with the c o n d u c t i v i t y data (3) and allows us to obtain good i n f o r m a t i o n on the behavior of the microscopic s t r u c t u r e o f these glasses with increasing Agl concentration. EXPERIMENTAL PROCEDURE AND RESULTS The (Agl)x(Ag20 - 2B203)l_x glasses were prepared according to the procedure p r e v i o u s l y described (3, 4~. X-ray d i f f r a c t i o n confirmed t h e i r amorphous nature. The absorption and v e l o c i t y of l o n g i t u d i n a l sound waves in the 5 to 45 Mhz and 80 to 470 k ranges were measured using the same apparatus described in r e f . ( l , 2). An epoxy resin was used to o b t a i n a good match between quartz transducers and the samples at temperatures as high as 470k. All the data have been corrected f o r a mean d i f f r a c t i o n loss of ~/a , 'la" being the transducer radius and "~" the ultrasound wavelength in the samples. Figure l shows the temperature behavior of acoustic a t t e n u a t i o n of 5 Mhz l o n g i t u d i n a l sound waves at various x. A broad peak is present in a l l the curves which show increases in height and s h i f t s to lower temperature with increasing Agl content. Moreover, the peak always s h i f t s to higher temperatures with increasing frequency which is t y p i c a l of t h e r m a l l y a c t i v a t e d r e l a x a t i o n s , see Figure 2. 0022-3093/83/0000-0000/$03.00 © 1983 North-Holland
G. Carini et al. /Internal friction due to mobile ions
394
Unfortunately, we were unable to see the peak at frequencies above 15 Mhz because of i t s high temperature (in the binary glass) and i t s very high attenuation (at high concentrations of Agl). However, i t can be seen from the experimental points in Fig. 2 that the peak also exists at higher frequencies. In Figure 3, is shown as a function of ultrasound frequencies as a logarithmic p l o t , having substracted a nearly temperature independent background. This reveals an f2 and fO,9 dependence, respectively on the r i g h t and l e f t hand side of the peak. The other glasses investigated show the same behavior. The 5 Mhz sound v e l o c i t y data, at room temperature, are inserted in Table I. They indicate that the introduction of Agl in Ag202B203 produces a less r i g i d structure in agreement with the corresponding decrease of TG (3). DISCUSSION From the peak temperature s h i f t with frequency, i t was possible to e x t r a c t the frequency factor ~ i and the apparent a c t i v a t i o n energies of the process, according to the r e l a t i o n s (5):
(I)
• X=O.O
,',
0.2
o
0.4
•
0.6
o =
o <:c
100
200
I
I
300
400
I,K Figure I .
Temperature dependence of acoustic attenuation in (Agl)x(Ag20.2B203)l_ x glasses.
G. Carini e t aL
/
In ternal friction due to mobile ions
395
derived from the Arrhenius equation. ~-i =
~le-E/kT
In eq. ( I ) and (2) T is the r e l a x a t i o n and TD2 is the peak temperature at the r e s p e c t i v e l y . The obtained values are maximum r e l a x a t i o n loss value Q~ak at r e l a t i o n between the i n t e r n a l f r i c t i o n temperature independent background has
(2)
time, k the Boltzmann constant, and Tpl ultrasound frequency of ~I or ~2, inserted in Table I together with the 5 Mhz t h a t was derived by the well-known and acoustic absorption (2). A nearly been subtracted.
The f o l l o w i n g remarks can be made: I . The a c t i v a t i o n energies decrease with Agl content and are very s i m i l a r to those obtained from d.c. c o n d u c t i v i t y measurements (3) in the same glasses. This shows t h a t the jumps of s i l v e r ions in the i n t e r s t i c e s of the network are r e a l l y the cause of the observed losses. 2. The disappearance of the peak observed in the b i n a r y glass, also in the form of a shoulder, in the high temperature t a i l of the peaks c h a r a c t e r i z i n g the A g l - r i c h glasses, indicates a decrease of the a c t i v a t i o n energy of i t s r e l a x i n g species due to the a d d i t i o n of Agl. This could agree with a recent hypothesis on i o n i c motion in these glasses (3). On the other hand, the sharp slope change shown from r e l a x a t i o n loss behavior, f o r x ~ 2 is not d i r e c t l y d i s c e r n i b l e on t h a t basis, Figure 4. At l e a s t q u a l i t a t i v e l y , i t is our opinion t h a t a s i m i l a r behavior is to be connected to some kind of a gradual s t r u c t u r a l modif i c a t i o n of the network induced by Agl. To analyze the peak q u a n t i t a t i v e l y , we have taken i n t o account the a t t e n u a t i o n due to a r e l a x i n g process with a s i n g l e r e l a x a t i o n time (5): O 0•
X=0.1
~---15 I
E
•
.£3 0•0 C 0
= io 3S,M
"
,
6~
•.6-,
•
• " •
25P1"~ •
-
• • •
15MhoZ• . 0 0
•
•
" 00 •
• 0•O
•
Oo
, 100
t
I 300
200
I
1
1,00
T, K Figure 2.
Acoustic a t t e n u a t i o n vs. temperature at various frequencies in the x = O.I glass. Note the temperature s h i f t of the peak.
396
G. Carini et al. / Internal friction due to mobile ions
--
D 2"V
~ 1 + ~2~2
(3)
being the r e l a x a t i o n time defined by eq. (2), v is the sound v e l o c i t y and D the r e l a x a t i o n strength. Using the data of Table I , we have obtained the curve represented by the dashed l i n e in Figure 5 f o r the x = 0.6 sample. The wider breadth of the experimental curve shows the existence of a r e l a x a t i o n time d i s t r i b u t i o n , confirming the r e s u l t found in s i m i l a r glasses. In order to account f o r t h i s , we assume t h a t the r e l a x a t i o n processes are associated with the ion jumps in double p o t e n t i a l wells of various b a r r i e r heights E. We also assume t h a t the d i s t r i b u t i o n arises from a d i s t r i b u t i o n of P(E) in the a c t i v a t i o n energy and a single value f o r To . In t h i s respect, the number of wells with a given b a r r i e r height E is p r o p o r t i o n a l to P(E) expressed from: _ I P(E} -(~-}1/2" ~ ' o ' e x p { - ( - ~ o E )2}
(4)
where Em and Eo are connected to the most probable value and to the width o f the d i s t r i b u t i o n , r e s p e c t i v e l y , Eq. (3) f o r the a t t e n u a t i o n is now modified in the f o l l o w i n g form (6). oo
a -- ~
B2 . I
-G
i NP(E)
OJ2~(E) dE
1+~2~2(E)
(5)
where N is the t o t a l number of jumping p a r t i c l e s per u n i t volume, B the deformation p o t e n t i a l , Q the d e n s i t y , v the ultrasound v e l o c i t y and x is given by eq. (2). The best f i t of 5 Mhz in x = 0.6 using eq. (5) is represented bx a continuous l i n e in Figure 5 and i t allowed us to determine Em, Eo, r o and NBc.
X=0.6 10
%
xl0 -3
/
. T= 370K / • T= 143 K ~
2O .21=
10
13
_ f.9
5
15 25
frequency, Mhz Figure 3. Logarithmic p l o t o f vs. frequency on the r i g h t and l e f t hand side of the peak.
I I I .2 .4 .6 Ag I content(mol.ar fraction) Figure 4: Maximum r e l a x a t i o n loss QZ~.~s a function o f Agl concentraton. The c ~ n uous l i n e is only i n d i c a t i v e o f the loss behavior in the x > 2 regions.
G. Carini et al. /Internal friction due to mobile ions
397
TABLE I Values of the apparent a c t i v a t i o n eDergy E, frequency f a c t o r , maximum r e l a x a t i o n loss QD~ak and 5 Mhz sound T O- i v e l o c i t y in (Agl)x(Ag20.2B203)l_ x glasses. molar fraction
E (eV mo1-1 )
$o-1
(sec -1}
0 -1 • 10 3 peak
v I (m/sec)
0.0
0.56
4 . 2 2 x 1014
6.35
4.33 x 10 3
0.1
0.51
3.35
6.77
4 11
0.2
0.48
2.75
8.58
3.97
0.4
0.41
2.65
15.6
3.54
0.6
0.33
2.55
20.6
2.98
Em = 0.31 eV/mol, Eo = 0.07 eV/mol, T~ I = lO14s -I and NB2 = 1.54 .1021 eV2/cm 3. This set of values was successively used to c a l c u l a t e (always by eq. 5) m at 15 Mhz, see the continuous l i n e in Figure 5. In t h i s case, the f i t between the t h e o r e t i c a l curve and experimental points is very good. The close s i m i l a r i t y o f Em (and also x - i ) with the corresponding values of Table I seems to i n d i c a t e t h a t the r e l ~ x a t i o n parameters, as e m p i r i c a l l y deduced,
E30 6
¢o
f-
N U
m o <
~_~1//// • _~__~ I 100
\\~%~_ ~-~_ I 300
-~15Mhz 5Mhz I I 500
T,K Figure 5.
Comparison between the experimental data ( s o l i d c i r c l e s ) and theoretical fit: - - - s i n g l e r e l a x a t i o n time, - - gaussian-like d i s t r i b u t i o n of a c t i v a t i o n energies (see t e x t ) .
398
G. Carini et al.
/ Internal friction due to mobile ions
can be assumed as the most probable values o f the d i s t r i b u t i o n ; however a more extensive analysis is necessary to confirm t h i s p o i n t . F i n a l l y , from the product NB2 we t r i e d to c a l c u l a t e the deformation p o t e n t i a l B assumiming t h a t , being in the presence of a r e l a t i v e l y large E d i s t r i b u t i o n , a l l the Ag+ ions present in the glass can c o n t r i b u t e to the r e l a x a t i o n loss. Using the Ag+ concentration (N - 1.4 . 1022cm-3) we obtain B = 0.33 eV, a value close to t h a t commonly observed in superionic (7) glasses. In conclusion we remark t h a t the existence of unusual losses in s i l v e r h a l i d e - s i l v e r borate glasses is to be connected with the t h e r m a l l y a c t i v a t e d jumps of Ag+ ions in the glassy m a t r i x . A q u a n t i t a t i v e analysis of acoustic a t t e n u a t i o n by a r e l a x a t i o n time d i s t r i b u t i o n allows us to deduce a set of parameters t h a t are reasonable w i t h the microscopic arrangement o f the ions. REFERENCES I. 2. 3. 4. 5. 6. 7.
G. C a r i n i , M. Cutroni, M. Federico, G. G a l l i , G. Tripodo and A. Avogadro, Physica B + C 107 (1981) 175. G. C a r i n i , M. Cutroni, M. Federico and G. G a l l i , Solid State Comm. 44 (1982) 1427. G. C h i o d e l l i , A. M a g i s t r i s , M. V i l l a and J. Bjorkstam, J. Non-Cryst. Solids, 51 (1982) 143. The authors are indebted to G. C h i o d e l l i and A. Magistris who have k i n d l y furnished the superionic glasses. A. S. Nowich and B. S. Berry, Anelastic Relaxation in C r y s t a l l i n e Solids, (Acad. Press, New York 1972) p. 57. S. Hunklinger and W. Arnold, in Physical Acoustics ed. by W. P. Mason and R. N. Thurston, (Academic Press, New York, 1976) p. 155. J. Y. Prieur and D. C i p l y s , Physics B + C 107 (1981) 181.