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Acoustic properties of borate glasses at low temperatures
Solid State Communications, Vol. 74, No. 7, pp. 661-665, 1990. Primed in Great Britain.
0038-1098/90 $3.00 + .00 Pergamon Press plc
ACOUSTIC PROPERTIES OF BORATE GLASSES AT LOW TEMPERATURES G. Carini, M. Cutroni, M. Federico, G. Galli and G. Tripodo Istituto di Fisica Generale dell'Universita' and Gruppo Nazionale di Struttura della Materia del C.N.R., 1-98100 Messina, Italy
(Received 24 January 1989 by R. Fieschi) Ultrasonic measurements were performed in A g 2 0 - B 2 0 3 glasses at low temperatures (1.5-30 K) in order to study the influence of the stoichiometry on the low energy excitations, generally represented in terms of two-level systems (TLS). The analysis of the acoustic attenuation, which is regulated by the mechanisms of the TLS-phonon assisted relaxation, permits to obtain the spectral density/5 of these excitations. The behaviour of/5 with Ag20 content is in contrast with the prediction of the free-volume theory. Moreover by considering the structural modifications of the glassy network, due to Ag20, the non-bridging oxygens, which are formed in relevant number when an high content of metallic oxide is added to boron oxide are suggested as main microscopic origin of TLS's the non-bridging oxygens, which are formed in relevant number when a high content of metallic oxide is added to boron oxide.
INTRODUCTION IT IS WELL known that glasses show anomalies in the acoustic, dielectric and thermal properties at low temperatures, which are well explained in terms of the tunneling model [1, 2]. This model is based on the existence of localized low energy excitations, probably arising from a tunneling motion of single atoms or a small group of atoms between near equivalent positions. These excitations, representing in terms of two level tunneling systems (TLS) with a splitting energy E, are characterized by their spectral density of states /5 (usually assumed as constant) and coupling constants with phonons Yt,However two questions are still open: the microscopic origin of the tunneling particle and the possibility of a correlation between/5 and the glass transition temperature TG. In fact some experimental evidence [3, 4] in quite a large class of glasses suggested a dependence/5 oc Ta ~. Moreover Cohen and Grest [6] supported these results by theoretical argumentation, connecting the TLS's to the presence of fre~-volume VI (low density regions) in the system. In the theory it is supposed that the cooling below the glass transition causes the freezing of voids in the glass. These voids provide the possibility of local motion to the neighbouring atoms, i.e. by tunneling at low temperatures. The TLS density of states should therefore depend from Vt and TG, i.e.
fi ~ ~IT~. More recently quite a stronger dependence has been proposed (7), /5 ~ exp (AIksT~) by considering the behaviour of the corresponding data in glasses with T6 spread in a wide interval. On the other hand the universality of the proposed correlation between /5 and Ta has been questioned in a number of papers, concerning the analysis of the TLS parameters extracted from thermal [8] and ultrasonic [9, 10] measurements. Now in a previous paper on the microscopic origin of TLS's in Agl-Ag20-B203 superionic glasses we have the impossibility of tunneling for silver ions. Taking into account the structure of these glasses (microdomains of Agl weakly bonded to the silver borate host matrix), it was inferred by experimental evidence that only the structural unit, present in the Ag20-B203 matrix contributes to TLS's. Tentatively the tetrahedral groups BO a or the nonbridging oxygens, which are formed when the silver oxide is added to boron oxide, were suggested as possible origin of TLS's. The aim of the present study was to extend the class of the investigated glasses of the Ag20-B203 system in order to recognize what kind of the cited structural units gives rise to TLS's. This glassy system is particularly suitable for this kind of analysis because specific structural information [11-13] is now available and the variation of the Ag20 content allows to change T, in a relatively large range.
661
662
ACOUSTIC P R O P E R T I E S OF BORATE GLASSES
Vol. 74, No. 7
O ~
f _ 1L
Y = 0.20
-•0
*90MHz
'T
-20
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."" • ~
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Fig. 1. Typical temperature behaviour of the attenua- Fig. 2. Temperature dependence of the fractional tion of longitudinal sound waves in (Ag20),(B203)l v sound velocity in (Ag20)~.(B203) 1 ~ glasses; - , glasses. y = 0.11; e , y = 20. In figure are als0 reported the values of the slope of the continuous lines. Note the shift of the vertical scale for the sample with y = 0.11. E X P E R I M E N T A L DETAILS Two glasses of the ( A g 2 0 ) v ( B 2 0 3 ) l - v system, with a molar fraction y of 0.11 and 0.2, were prepared by using the procedure elsewhere described [14]. The acoustic attenuation and the velocity of 10-90 MHz longitudinal sound waves was measured between 1.5 K and 30 K by the experimental set-up previously described [10]. All the attenuation data have been corrected for an average diffraction loss ~,/a 2 db c m ~, )~ being the ultrasonic wavelength and a the transducer radius. The loss, due to the bonding agent between the transducer and the sample, can be neglected due to its very thin thickness ( < 4/~m).
RESULTS A N D DISCUSSION In Fig. 1 we show the temperature dependence of the acoustic attenuation in the (Ag20)0.2(B203)0. s sample. A similar behaviour has also been revealed in the other investigated glass ( y = 0.11). The attenuation increases with the temperature, after showing a temperature independent but frequency dependent plateau. At higher temperatures, the loss tends to increase quite monotonically. In Fig. 2 the fractional variation of the sound velocity ( v ( T ) - vo)/Vo, v• being the value at the lowest temperature, is plotted as a function of T. Initially the velocity is almost constant, showing for higher T a logarithmic decrease and then tending to bend. Both the plateau in the acoustic attenuation and the logarithmic decrease of A v / v are expected to arise from the TLS phonon-assisted relaxation [15]. In fact from this process, in the limit of higher tempera-
tures when ~o T~nin "~ 1
=
=
2v-
(l)
and at low temperatures, when co T~ dn >> 1 ~4 G ~i
--
96 vi
k 3 T 3.
(2)
In the expression (1) and (2) the index i refers to the different polarizations, v is the sound velocity, a~ the angular frequency, T the absolute temperature, p the density, ? the deformation potential, k 3 a constant which depends on the deformation potential and T~"i" is the minimum relaxation time, characterizing the process (a Ti distribution is to be considered, owing to the randomness of the network). In the explored temperature range, the sound velocity is regulated by the relaxational and resonant interaction of TLS's with phonons [10] and its behaviour can be expressed as Av _v
nCiln{~0}.
(3)
To being an arbitrary reference temperature and n a parameter equal to 1/2 or 5/2, depending on whether TLS's relax by a one or two-phonon process [16]. Now the frequency dependence of the acoustic attenuation in the plateau region is slightly stronger than the linear one, as it is shown from the logarithmic plot in Fig. 3. It has been proved [9], however, that the additional contribution comes from loss mechanisms, which have anf"-dependence, being m > 1, and only TLS relaxation contributes linearly.
663
A C O U S T I C P R O P E R T I E S OF B O R A T E GLASSES
Vol. 74, No. 7
f}.25
+I f
--'-2O 'E
.2o
v.
u m
8
o
/
(
O
5O
I I00
Frequency(MHz)
8
( 20
I
I
50 100 Frequency(MHz)
Fig. 3. Frequency dependence of the acoustic attenuation in the plateau region. A plot of elf as a function of f reveals a n f2 contribution as dominant in the background attenuation, see Fig. 4, and allows determination of the coefficient of the linear term by extrapolating the curve at f = 0. The expression of this coefficient is given by equation (1) and the obtained values of Cl and/5 7~ are inserted in Table 1. By subtracting the acoustic background from the experimental data, it was possible to verify the lack of the behaviour, expected by equation (2). It appears that the co T~ ~" > 1 region is at lower temperatures. Concerning the velocity data the logarithmic decrease just falls in the temperature region where the attenuation plateau is present and the condition co T~ i" ~ 1 is satisfied. The slope is - 1 0 . 0 x 10 -4 for the glass with y = 0.11 and - 1 3 . 5 x 10 -4 for that with y = 0.20. These values do not correspond exactly to 5/2 of the C[s, deduced from the attenuation data, but surely we can exclude the value 1/2 for the coefficient n which appears in equation (3). This
Fig. 4. Frequency behaviour of the ratio between the acoustic attenuation and the ultrasohnd frequency in the plateau region.
peculiarity indicates that the one-phonon process is not the dominant one in the high temperature region of the TLS relaxation.In order to obtain the density of states /5 from the products /5 7~, it is necessary to know the corresponding values of the coupling constants 7t- N o w it has been found that a rough correlation exists between the parameters 7i and the glass transition temperature TG for a wide class of glasses [4, 7]. The best linear fit of these data [10] permitted us to extract the values of ~ corresponding to T~'s of our glasses. They are inserted in Table 1 together with the TLS densities of states /5, consequently obtained. In Table 1 the value of/5 for the y = 0.5 glass is also inserted. It has been derived by a linear extrapolation of the data, obtained for x >~ 0.3 in samples of the (Agl)x((Ag20)0.5(B203)0.5) j_x system. The extrapolation is necessary because the y = 0.5 composition is located outside of the miscibility range [23] and consequently it is impossible to prepare a similar glass in homogeneous form. However the structure of this
Table 1. Values of density p sound velocity v, parameters C and/572 coupling constant 7~, TLS density of states /5, glass transition temperature Ta and the density of BOg tetrahedral groups (N4) non-bridging oxygens (NBO) ['or (Ag20),(B203) I ,. The values of p and TG are those of[23] y
p v (grcm 3) ( m s ')
C*104
/57~ Yl (108ergscm 3) (eV)
/5 (1032ergs l c m 3)
Tc (K)
N4 NBO (1022cm 3) (1021cm 3)
0.00 0.11 0.20 0.33 0.50
1.80 2.60 3.28 4.03 5.45 c
2.4 b 4.83 3.97 5.68 -
0.51 1.93 2.46 4.47 -
4.5" 1.96 1.90 3.36 9.30 ~
485 573 658 663 -
0,419 0.817 1.141 1.261
3470 3973 4350 4420 -
~ see [16]. b see [18]. ~ Extrapolated values.
0.21 b 0.62 0.71 0.72 -
0.156 0.217 1.963 9.146
664
ACOUSTIC P R O P E R T I E S OF BORATE GLASSES
glass has been studied by molecular dynamics [12] and its consideration makes to the discussion on the microscopic origin of TLS's in borate glasses, more complete. It is to be noted that the value of/5 for the boron dioxide is derived from specific heat measurements [17] and in order to make a comparison with those obtained from ultrasonic measurements, only a fraction (-~ 1/10) of it should be considered. In fact it was pointed out [18, 20] that only the TLS's, strongly coupled with phonons and characterized by a fast relaxation rate, will be involved in ultrasonic or thermal conductivity experiments. Keeping these considerations in mind, we can observe t h a t / 5 increases with the Ag20 content and with Ta, ruling out the validity of the proposed correlations between /5 and T(; for silver borate glasses. We would like to underline that our conclusions agree with the ones obtained from thermal [8] and ultrasonic [10, 19] studies in alkaline borate and silver halides-silver borate glasses. These results added to those of a recent review of the TLS characteristics in glassy oxides, semiconductors and polymers [9] point out that the connection between the free-volume and TLS's as suggested from the theory, can not be considered as a general trend of the glassy state in its actual form. The prediction about the independence of the total number of the TLS's from the stoichiometry, especially appears to be questionable. At present it is quite difficult to evaluate quantitatively the dependence of the density of the tunneling centers N on the material, and at most qualitatively we like to underline that in borate glasses the introduction of metallic oxide stiffens the structure [14, 21] and the increasing Ta is a clear evidence, but it causes also an increasing degree of local molecular mobility. As pointed out from N M R [22] and MD [12] studies, the oxygens introduced by the metallic oxide link the planar units BO3, typical of B203, and transform them into tetrahedral groups BO4. Moreover, particularly at high content of metallic oxide (y >~ 0.3) the B O 4 formation rate tends to decrease and nonbridging oxygens (NBO) are formed, namely oxygens not linking various structural units (BO3 o r B O a ) , but connected to a single boron ion. The silver ions are localized in the interstices of the network, near the BO4 groups or the NBO's to ensure charge neutrality. Thermally activated local motions are associated to both structural units cited, as shown from the relaxation peaks, which appear in the mechanical spectra [21, 23] and have been attributed to them. Now this situation could be reflected in an increasing tunneling activity at low temperatures, because a high number of particles can be involved in the tunneling motion.
Vol. 74, No. 7
Consequently the increase of T~ could be covered by a faster increase of N, resulting in a higher /5. Finally, in order to discuss the possible microscopic origin of TLS's in borate glasses we have to distinguish between the effects of extrinsic (impurities) and intrinsic tunneling states, because this kind of glasses contains a relevant amount of OH groups, when prepared without appropriate controlled atmosphere conditions (our case). In fact it has been evaluated [21, 23] that the OH amount is about 1.1% by weight for pure B203 and decreases to a value between 0.4% and 0.1% by weight by adding Ag20, following a decreasing solubility of water with the silver oxide. However there is evidence in dielectric glasses [25] that the presence of OH groups does not influence the low temperature acoustic properties and consequently we suppose that this finding can also be extended to borate glasses. Now bearing in mind that a value of/5 for B203 must be appropriately scaled, the increase of/5 with Ag20 should be associate with the structural units, which are formed when the metallic oxide is added. Since the possibility of tunneling for silver ions has been excluded [10], only the BO4 groups or the NBO's must be considered. Particularly, if the TLS's arise from atomic motion, it seems that the atoms which are suggested as being responsible for the high temperature acoustic anomalies, as the oxygen atoms in BO4 groups and the NBO's [21,23, 26] could mainly be subjected to a tunneling local motion. Of course the present discussion on the microscopic origin of TLS's is based on more or less general considerations, which up to now could neither be verified nor contradicted. Its aim is to find, at most qualitatively a unified microscopic explanation for the low and high temperature acoustic anomalies, which is a view recently proposed by an interesting theoretical model [27]. We have calculated the density of BO4 groups and NBO's by using the MD results, see Table 1. The B O 4 tetrahedron number seem to be an increasing function of y, while the NBO number keeps small and constant for y < 0.33 and increases sharply for y /> 0.33. It seems that the behaviour of/5 well reflects the one of NBO's and in the hypothesis of atomic motion as origin of TLS, we conclude that the contribution of NBO's among the particles which participate in the TLS's could be considered the most relevant. It is worth observing that the same remarks can be inferred from the analysis of the /5 values in lithium borate glasses [19]. REFERENCES
1.
P.W. Anderson, B.L. Halperin & C.M. Varma, Phil. Mag. 25, 1 (1972).
Vol. 74, No. 7 2. 3. 4, 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
ACOUSTIC PROPERTIES OF BORATE GLASSES
W.A. Phillips, J. Low Temp. Phys. 7, 351 (1972). C.L. Reynolds Jr. J. Non Cryst. Solids 30, 371 (1979). P. Doussineau, M. Matecki & W. Schon, J. Phys. Colloq. 43, C9-493 (1982); J. Phys. (Paris) 44, 101 (1983). W.M. MacDonald, A.C. Anderson & J. Schroder, Phys. Rev. B31, 1090 (1985). M.H. Cohen & G.S. Grest, SolidState Commun. 39, 143 (1981). N. Reichert, M. Shmidt & S. Huklinger, Solid State Commun. 57, 315 (1986). W.M. MacDonald & A. C. Anderson, Phys. Rev. B 1208 (1985). J.F. Berret & M. Meigner, Zeit,fur Phys. B 70, 65 (1988). G. Carini, M. Cutroni, M. Federico & G. Tripodo, Phys. Rev. B37, 7021 (1988). K.S. Kim & P.J. Bray, J. Non Metals 2, 95 (1974). M . C . Abramo, G. Carini & G. Pizzimenti, J. Phys. C: Solid State 21, 527 (1988). G.D.'Alba, P. Fornasini, F. Rocca, E. Bernieri, E. Burattini & S. Mobilio, J. Non. Cryst. Solids 91, 153 (1987). G. Carini, M. Cutroni, M. Federico, G. Galli & G. Tripodo, Phys. Bey. B30, 7219 (1984). J. Jackle, Zeit, Phys. 257, 212 (1972).
16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
665
P. Doussineau, Ch. Frenois, R. Leisure, A, Levelut & J. Y. Prieur, J. Phys. (Paris) 41, 1193 (198o). R.B. Stephens, Phys. Rev. B13, 852 (1976). A.C. Anderson, in Amorphous Solids (Edited by W.A. Phillips), Springer, Berlin (1981). M. Devand, J.Y. Prieur & W.D. Wallace, Solid State Ionics, 9-10, 593 (1983). J.L. Black & B.I. Halperin, Phys. Rev. B16, 2879 (1977). J.T. Krause & C.R. Kurkjian, in Borate Glasses (Edited by L.D. Pye, V.D. Frechette & N.J. Kreidl), Plenum Press, New York 577 (1977). P.J. Bray, in Borate Glasses (Edited by L.D. Pye, V.D. Frechette & N.J. Kreidl), Plenum Press, New York, 321, (1977). E.N. Boulos & N.J. Kreidl, J. Am. Ceram. Soc. 54, 368 (1971). G. Chiodelli, A. Magistris, M. Villa & J. Bjorkstare, J. Non Cryst. Solids" 51, 143 ,(1982). S. Hunklinger, L. Piche', J. C. Lasjaunias & K. Dransfield, J. Phys. C: Solid State 8, 423 (1975). R.E. Strakna & H.T. Savage, J. Appl. Phys. 35, 1445 (1964). V.N. Fleurov & L.I. Trakhtenberg, J. Phys. C: Solid State 19, 5529 (1986).
0038-1098/90 $3.00 + .00 Pergamon Press plc
ACOUSTIC PROPERTIES OF BORATE GLASSES AT LOW TEMPERATURES G. Carini, M. Cutroni, M. Federico, G. Galli and G. Tripodo Istituto di Fisica Generale dell'Universita' and Gruppo Nazionale di Struttura della Materia del C.N.R., 1-98100 Messina, Italy
(Received 24 January 1989 by R. Fieschi) Ultrasonic measurements were performed in A g 2 0 - B 2 0 3 glasses at low temperatures (1.5-30 K) in order to study the influence of the stoichiometry on the low energy excitations, generally represented in terms of two-level systems (TLS). The analysis of the acoustic attenuation, which is regulated by the mechanisms of the TLS-phonon assisted relaxation, permits to obtain the spectral density/5 of these excitations. The behaviour of/5 with Ag20 content is in contrast with the prediction of the free-volume theory. Moreover by considering the structural modifications of the glassy network, due to Ag20, the non-bridging oxygens, which are formed in relevant number when an high content of metallic oxide is added to boron oxide are suggested as main microscopic origin of TLS's the non-bridging oxygens, which are formed in relevant number when a high content of metallic oxide is added to boron oxide.
INTRODUCTION IT IS WELL known that glasses show anomalies in the acoustic, dielectric and thermal properties at low temperatures, which are well explained in terms of the tunneling model [1, 2]. This model is based on the existence of localized low energy excitations, probably arising from a tunneling motion of single atoms or a small group of atoms between near equivalent positions. These excitations, representing in terms of two level tunneling systems (TLS) with a splitting energy E, are characterized by their spectral density of states /5 (usually assumed as constant) and coupling constants with phonons Yt,However two questions are still open: the microscopic origin of the tunneling particle and the possibility of a correlation between/5 and the glass transition temperature TG. In fact some experimental evidence [3, 4] in quite a large class of glasses suggested a dependence/5 oc Ta ~. Moreover Cohen and Grest [6] supported these results by theoretical argumentation, connecting the TLS's to the presence of fre~-volume VI (low density regions) in the system. In the theory it is supposed that the cooling below the glass transition causes the freezing of voids in the glass. These voids provide the possibility of local motion to the neighbouring atoms, i.e. by tunneling at low temperatures. The TLS density of states should therefore depend from Vt and TG, i.e.
fi ~ ~IT~. More recently quite a stronger dependence has been proposed (7), /5 ~ exp (AIksT~) by considering the behaviour of the corresponding data in glasses with T6 spread in a wide interval. On the other hand the universality of the proposed correlation between /5 and Ta has been questioned in a number of papers, concerning the analysis of the TLS parameters extracted from thermal [8] and ultrasonic [9, 10] measurements. Now in a previous paper on the microscopic origin of TLS's in Agl-Ag20-B203 superionic glasses we have the impossibility of tunneling for silver ions. Taking into account the structure of these glasses (microdomains of Agl weakly bonded to the silver borate host matrix), it was inferred by experimental evidence that only the structural unit, present in the Ag20-B203 matrix contributes to TLS's. Tentatively the tetrahedral groups BO a or the nonbridging oxygens, which are formed when the silver oxide is added to boron oxide, were suggested as possible origin of TLS's. The aim of the present study was to extend the class of the investigated glasses of the Ag20-B203 system in order to recognize what kind of the cited structural units gives rise to TLS's. This glassy system is particularly suitable for this kind of analysis because specific structural information [11-13] is now available and the variation of the Ag20 content allows to change T, in a relatively large range.
661
662
ACOUSTIC P R O P E R T I E S OF BORATE GLASSES
Vol. 74, No. 7
O ~
f _ 1L
Y = 0.20
-•0
*90MHz
'T
-20
~_ , 6
+ 70 MHz
."" • ~
_o
e
~-20
+
+
+
+
•
o -40 x
.+++* s+ +
*'*'*'*'*'*'*'*'*'~*-10.-40.10 Ae
~
• 501"lHz
•
o
-60
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t
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1
5
__
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I
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15
I
20
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I
2
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_ _ L
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_ _
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50
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Fig. 1. Typical temperature behaviour of the attenua- Fig. 2. Temperature dependence of the fractional tion of longitudinal sound waves in (Ag20),(B203)l v sound velocity in (Ag20)~.(B203) 1 ~ glasses; - , glasses. y = 0.11; e , y = 20. In figure are als0 reported the values of the slope of the continuous lines. Note the shift of the vertical scale for the sample with y = 0.11. E X P E R I M E N T A L DETAILS Two glasses of the ( A g 2 0 ) v ( B 2 0 3 ) l - v system, with a molar fraction y of 0.11 and 0.2, were prepared by using the procedure elsewhere described [14]. The acoustic attenuation and the velocity of 10-90 MHz longitudinal sound waves was measured between 1.5 K and 30 K by the experimental set-up previously described [10]. All the attenuation data have been corrected for an average diffraction loss ~,/a 2 db c m ~, )~ being the ultrasonic wavelength and a the transducer radius. The loss, due to the bonding agent between the transducer and the sample, can be neglected due to its very thin thickness ( < 4/~m).
RESULTS A N D DISCUSSION In Fig. 1 we show the temperature dependence of the acoustic attenuation in the (Ag20)0.2(B203)0. s sample. A similar behaviour has also been revealed in the other investigated glass ( y = 0.11). The attenuation increases with the temperature, after showing a temperature independent but frequency dependent plateau. At higher temperatures, the loss tends to increase quite monotonically. In Fig. 2 the fractional variation of the sound velocity ( v ( T ) - vo)/Vo, v• being the value at the lowest temperature, is plotted as a function of T. Initially the velocity is almost constant, showing for higher T a logarithmic decrease and then tending to bend. Both the plateau in the acoustic attenuation and the logarithmic decrease of A v / v are expected to arise from the TLS phonon-assisted relaxation [15]. In fact from this process, in the limit of higher tempera-
tures when ~o T~nin "~ 1
=
=
2v-
(l)
and at low temperatures, when co T~ dn >> 1 ~4 G ~i
--
96 vi
k 3 T 3.
(2)
In the expression (1) and (2) the index i refers to the different polarizations, v is the sound velocity, a~ the angular frequency, T the absolute temperature, p the density, ? the deformation potential, k 3 a constant which depends on the deformation potential and T~"i" is the minimum relaxation time, characterizing the process (a Ti distribution is to be considered, owing to the randomness of the network). In the explored temperature range, the sound velocity is regulated by the relaxational and resonant interaction of TLS's with phonons [10] and its behaviour can be expressed as Av _v
nCiln{~0}.
(3)
To being an arbitrary reference temperature and n a parameter equal to 1/2 or 5/2, depending on whether TLS's relax by a one or two-phonon process [16]. Now the frequency dependence of the acoustic attenuation in the plateau region is slightly stronger than the linear one, as it is shown from the logarithmic plot in Fig. 3. It has been proved [9], however, that the additional contribution comes from loss mechanisms, which have anf"-dependence, being m > 1, and only TLS relaxation contributes linearly.
663
A C O U S T I C P R O P E R T I E S OF B O R A T E GLASSES
Vol. 74, No. 7
f}.25
+I f
--'-2O 'E
.2o
v.
u m
8
o
/
(
O
5O
I I00
Frequency(MHz)
8
( 20
I
I
50 100 Frequency(MHz)
Fig. 3. Frequency dependence of the acoustic attenuation in the plateau region. A plot of elf as a function of f reveals a n f2 contribution as dominant in the background attenuation, see Fig. 4, and allows determination of the coefficient of the linear term by extrapolating the curve at f = 0. The expression of this coefficient is given by equation (1) and the obtained values of Cl and/5 7~ are inserted in Table 1. By subtracting the acoustic background from the experimental data, it was possible to verify the lack of the behaviour, expected by equation (2). It appears that the co T~ ~" > 1 region is at lower temperatures. Concerning the velocity data the logarithmic decrease just falls in the temperature region where the attenuation plateau is present and the condition co T~ i" ~ 1 is satisfied. The slope is - 1 0 . 0 x 10 -4 for the glass with y = 0.11 and - 1 3 . 5 x 10 -4 for that with y = 0.20. These values do not correspond exactly to 5/2 of the C[s, deduced from the attenuation data, but surely we can exclude the value 1/2 for the coefficient n which appears in equation (3). This
Fig. 4. Frequency behaviour of the ratio between the acoustic attenuation and the ultrasohnd frequency in the plateau region.
peculiarity indicates that the one-phonon process is not the dominant one in the high temperature region of the TLS relaxation.In order to obtain the density of states /5 from the products /5 7~, it is necessary to know the corresponding values of the coupling constants 7t- N o w it has been found that a rough correlation exists between the parameters 7i and the glass transition temperature TG for a wide class of glasses [4, 7]. The best linear fit of these data [10] permitted us to extract the values of ~ corresponding to T~'s of our glasses. They are inserted in Table 1 together with the TLS densities of states /5, consequently obtained. In Table 1 the value of/5 for the y = 0.5 glass is also inserted. It has been derived by a linear extrapolation of the data, obtained for x >~ 0.3 in samples of the (Agl)x((Ag20)0.5(B203)0.5) j_x system. The extrapolation is necessary because the y = 0.5 composition is located outside of the miscibility range [23] and consequently it is impossible to prepare a similar glass in homogeneous form. However the structure of this
Table 1. Values of density p sound velocity v, parameters C and/572 coupling constant 7~, TLS density of states /5, glass transition temperature Ta and the density of BOg tetrahedral groups (N4) non-bridging oxygens (NBO) ['or (Ag20),(B203) I ,. The values of p and TG are those of[23] y
p v (grcm 3) ( m s ')
C*104
/57~ Yl (108ergscm 3) (eV)
/5 (1032ergs l c m 3)
Tc (K)
N4 NBO (1022cm 3) (1021cm 3)
0.00 0.11 0.20 0.33 0.50
1.80 2.60 3.28 4.03 5.45 c
2.4 b 4.83 3.97 5.68 -
0.51 1.93 2.46 4.47 -
4.5" 1.96 1.90 3.36 9.30 ~
485 573 658 663 -
0,419 0.817 1.141 1.261
3470 3973 4350 4420 -
~ see [16]. b see [18]. ~ Extrapolated values.
0.21 b 0.62 0.71 0.72 -
0.156 0.217 1.963 9.146
664
ACOUSTIC P R O P E R T I E S OF BORATE GLASSES
glass has been studied by molecular dynamics [12] and its consideration makes to the discussion on the microscopic origin of TLS's in borate glasses, more complete. It is to be noted that the value of/5 for the boron dioxide is derived from specific heat measurements [17] and in order to make a comparison with those obtained from ultrasonic measurements, only a fraction (-~ 1/10) of it should be considered. In fact it was pointed out [18, 20] that only the TLS's, strongly coupled with phonons and characterized by a fast relaxation rate, will be involved in ultrasonic or thermal conductivity experiments. Keeping these considerations in mind, we can observe t h a t / 5 increases with the Ag20 content and with Ta, ruling out the validity of the proposed correlations between /5 and T(; for silver borate glasses. We would like to underline that our conclusions agree with the ones obtained from thermal [8] and ultrasonic [10, 19] studies in alkaline borate and silver halides-silver borate glasses. These results added to those of a recent review of the TLS characteristics in glassy oxides, semiconductors and polymers [9] point out that the connection between the free-volume and TLS's as suggested from the theory, can not be considered as a general trend of the glassy state in its actual form. The prediction about the independence of the total number of the TLS's from the stoichiometry, especially appears to be questionable. At present it is quite difficult to evaluate quantitatively the dependence of the density of the tunneling centers N on the material, and at most qualitatively we like to underline that in borate glasses the introduction of metallic oxide stiffens the structure [14, 21] and the increasing Ta is a clear evidence, but it causes also an increasing degree of local molecular mobility. As pointed out from N M R [22] and MD [12] studies, the oxygens introduced by the metallic oxide link the planar units BO3, typical of B203, and transform them into tetrahedral groups BO4. Moreover, particularly at high content of metallic oxide (y >~ 0.3) the B O 4 formation rate tends to decrease and nonbridging oxygens (NBO) are formed, namely oxygens not linking various structural units (BO3 o r B O a ) , but connected to a single boron ion. The silver ions are localized in the interstices of the network, near the BO4 groups or the NBO's to ensure charge neutrality. Thermally activated local motions are associated to both structural units cited, as shown from the relaxation peaks, which appear in the mechanical spectra [21, 23] and have been attributed to them. Now this situation could be reflected in an increasing tunneling activity at low temperatures, because a high number of particles can be involved in the tunneling motion.
Vol. 74, No. 7
Consequently the increase of T~ could be covered by a faster increase of N, resulting in a higher /5. Finally, in order to discuss the possible microscopic origin of TLS's in borate glasses we have to distinguish between the effects of extrinsic (impurities) and intrinsic tunneling states, because this kind of glasses contains a relevant amount of OH groups, when prepared without appropriate controlled atmosphere conditions (our case). In fact it has been evaluated [21, 23] that the OH amount is about 1.1% by weight for pure B203 and decreases to a value between 0.4% and 0.1% by weight by adding Ag20, following a decreasing solubility of water with the silver oxide. However there is evidence in dielectric glasses [25] that the presence of OH groups does not influence the low temperature acoustic properties and consequently we suppose that this finding can also be extended to borate glasses. Now bearing in mind that a value of/5 for B203 must be appropriately scaled, the increase of/5 with Ag20 should be associate with the structural units, which are formed when the metallic oxide is added. Since the possibility of tunneling for silver ions has been excluded [10], only the BO4 groups or the NBO's must be considered. Particularly, if the TLS's arise from atomic motion, it seems that the atoms which are suggested as being responsible for the high temperature acoustic anomalies, as the oxygen atoms in BO4 groups and the NBO's [21,23, 26] could mainly be subjected to a tunneling local motion. Of course the present discussion on the microscopic origin of TLS's is based on more or less general considerations, which up to now could neither be verified nor contradicted. Its aim is to find, at most qualitatively a unified microscopic explanation for the low and high temperature acoustic anomalies, which is a view recently proposed by an interesting theoretical model [27]. We have calculated the density of BO4 groups and NBO's by using the MD results, see Table 1. The B O 4 tetrahedron number seem to be an increasing function of y, while the NBO number keeps small and constant for y < 0.33 and increases sharply for y /> 0.33. It seems that the behaviour of/5 well reflects the one of NBO's and in the hypothesis of atomic motion as origin of TLS, we conclude that the contribution of NBO's among the particles which participate in the TLS's could be considered the most relevant. It is worth observing that the same remarks can be inferred from the analysis of the /5 values in lithium borate glasses [19]. REFERENCES
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