- Email: [email protected]
Study of nuclear spin relaxation in CLAP glasses
] O U R N A L OF
Journal of Non-Crystalline Solids 172-174 (1994) 1373-1377
ELSEVIER
Study of nuclear spin relaxation in CLAP glasses R. K f i c h l e r a, O . K a n e r t a, M . F r i c k e a, H . J a i n b, K . L . N g a i c'* a Institute of Physics, University of Dortmund, Dortmund, German)' b LeHigh University, Bethlehem, PA, USA c Naval Research Laboratory, Code 6807, Washington, DC 20375-5000, USA
Abstract
19F nuclear spin relaxation (NSR) rates are reported at various frequencies between room temperature and about 800 K, i.e., below and above the glass transition temperature, T~_-__570K, for glasses of the general composition CdF2-LiF-A1F3 PbF2 (CLAP glasses). The observed NSR rate comes from three different contributions. These contributions are related to degrees of freedom of the F- ions, and are compared with conductivity data performed by Moynihan and co-workers on the same glass.
1. Introduction
Recent conductivity experiments carried out by Moynihan and co-workers show an uncommon decrease of the exponent fl of the KohlrauschWilliams-Watts (KWW) function ~(t) = e x p [ - (t/z) ~] with increasing temperature above the glass transition temperature, Tg, in CLAP glasses [1]. This unusual temperature dependence of fl has been seen before only in the glass-forming molten salt 0.4Ca(NO3)2-0.6KNO3 (CKN) above its glass transition temperature [2,3]. In view of the drastic difference in chemical composition of these two glass-forming ionic materials, this unusual behavior being commonly shared by them is interesting and it warrants further investigation. Such further investigations may eventually lead us to a bet-
* Corresponding author. Tel: + 1-2027676150. Telefax: + 1202 7670546.
ter understanding of the dynamics of diffusion of ions in them. The anomalous behavior of fl in C K N has remained unexplained until a recent attempt in the framework of the coupling model [4]. The key observation in this explanation is that R , ( T ) = (rs(T))/(%(T)), defined as the ratio of the average structural relaxation time, (%(T)), to the average conductivity relaxation time, (%(T)), at T - - Tg is only about 104 in C K N (compared with 101°-10 ~4 in alkali silicate glasses and fast ionic conductors). Further, when T is increased above Tg, Re(T) decreases towards 1. Thus, there is a temperature region above Tg in C K N where a broad crossover from coupled to decoupled structural and conductivity relaxations occur. At sufficiently high temperature above T~ when Re is close to 1, structural relaxation and conductivity relaxation are fully coupled together. Non-exponentiality of the structural relaxation as described by the stretch exponent, fl(T), of the KWW structural relaxation function is determined by the cooperative rearrangement dynamics of basic structural units.
0022-3093/94/$07.00 © 1994 ElsevierScience B.V. All rights reserved SSDI 0 0 2 2 - 3 0 9 3 ( 9 4 ) 0 0 0 5 1 - N
1374
R. Kiichler et al. / Journal of Non-Crystalline Solids 172-174 (1994) 1373-1377
Since the structural relaxation and conductivity relaxation are fully coupled, i.e., R d T ) ~ I , the stretch exponent fl~(T) of conductivity relaxation becomes the same as fls(T) of structural relaxation. For CKN, the condition Re ~ 1 holds at high temperatures and remains approximately valid down to T ~ 100°C at which from mechanical measurements fls = 0.52 and fl~ = 0.48 from conductivity relaxation measurements [5]. The two stretch exponents are essentially equal as expected because their common origin is the cooperative dynamics of structural relaxation. On further decrease of T below 100°C towards Tg, Re(T) starts to increase rapidly to reach 104 at T = Tg, indicating that at the same time the conductivity relaxation is also increasingly decoupled from the structural relaxation. When the conductivity relaxation is totally decoupled from the structural relaxation (i.e., when R,>>I), its non-exponentiality or fl~ is no longer determined by the cooperative coupled dynamics of structural relaxation but now instead by the interactions between the ions and counterions in the molten salt. It can be safely assumed that this change in mechanism is realized at T = Tg when R ~ 1 0 4 and the experimentally found value of ft,(Tg) = 0.74 can be defined with the stretch exponent caused by mutual interactions between the ions alone in CKN. Thus, as the melt is cooled from about 150°C down to Tg, the origin of fl~ starts from being purely structural relaxation dynamics which has a stretch exponent of 0.52, then shifts gradually to being a mixture of both mechanisms, and finally to being entirely due to interactions between the ions which has the value of 0.72 for CKN. As a consequence, ft, has to exhibit the anomalous increase with decreasing temperature as
observed in CKN. It would be interesting to see if this explanation holds also for CLAP glasses. The fact that CLAP glasses also have comparable values of decoupling index, Rd T), at Tg and similar temperature dependence is an encouraging sign for such a possibility. In general conductivity data can be better understood when complemented by nuclear spin relaxation (NSR) measurements. In order to obtain further information about the subject, we have performed 19F NSR measurements between room temperature and about 800 K on a CLAP glass of the same composition as used for the conductivity experiments. For comparison, we have carried out a d d i t i o n a l 19F NSR experiments on a fluorozirconate glass in the same temperature range. The exact compositions of the two glasses are listed in Table 1. It has to be remarked that the 19F nuclear probe has a spin I = 1/2, i.e., the observed NSR rates are caused by fluctuations of nuclear magnetic dipole-dipole interactions between the 19F probes (I-! interaction) and between the ~9F probes and other magnetic species in the sample such as 2TA1, VLi, etc. (I-S interaction). To the contrary, because of the missing nuclear quadrupole moment of 19F, fluctuations of electric field gradients due to moving charges do not contribute to the NSR process. As shown in Fig. 1, the time evolution of the 19F nuclear magnetization in the laboratory frame (Zeeman relaxation T1) as well as in the rotating frame (rotating frame relaxation T~p) obeys an exponential law to a good approximation. From the slopes of the decay, the corresponding NSR rates 1/T~ and 1/T~p, respectively, were calculated.
2. Experimental results
Table 1 Properties of glasses investigated Sample
Composition (mol%)
Tg (K)
T¢,y~tal(K)
CLAP
9.5CDF2-11.5CdO -3CdC12-6LiF-4KF -30AIFa-30PbF2-4YF3 -2LaF3
500580
770
ZBLALi
48ZrF4-22BaF2 -5LaF3-4A1F3-21 LiF
528
630
Fig. 2 exhibits the temperature dependence of the 19F NSR rates in the CLAP glass observed at three different frequencies. Further, for comparison the figure shows ~9FNSR data in the ZBLALi glass measured at 56.38 MHz. Obviously, the CLAP data differ remarkably from the NSR data in ZBLALi. The latter can be interpreted in terms of a common approach used for various oxide and
R. Kiichler et al. / Journal o f Non-Crystalline Solids 172 174 (1994) 1373-1377 I
i
~T
i
i
336K
=
T[K] 800
600
=m= v
O.
N"
=
1 02
1375
496. m s
500
400
300
% lie
1 03
=~=.=
E
l= l= •
tO
• =•
¢-
I
T1 p= 6 . 5 4 m~
1 01
1 01
•
"
°
~
*e
• •0°
o
I
I
'i '
time [arb. units]
o o e •
o o • •
ZBLALi •
i
',Tg
•
A A •
56.38 MHz
• " • • A • ~,
i
1 0 "1 I
1.0
o(~eo
•
,
Fig. 1. Decay of 19F nuclear magnetization in the laboratory frame, mz(t), and in the rotating frame, rap(t), for CLAP glass. Decays are exponential in the measured temperature region.
•
i
I 00
I
56.38 MHz
oo
eo oo•O ~e%eeoeJeeeee e i •
I
•
CLAP • 52 kHz o 23.31 MHz
o ,Do • ".o II o ,
O'l
E
=
Tg
1 02
N
1.5
i
• I
I
I
2.0
2.5
3.0
3.5
1 / T [1 0 .3 K 1 ]
Z r - F glasses [6]:
(1)
1/T1 = l/Tlla + 1/Tllb.
Here, 1/Tll, denotes a low-temperature NSR process due to low-frequency excitations (LFE) of disorder modes intrinsic to the glassy state of matter. The process is commonly described by the asymmetric double-well potential (ADWP) model leading in first approximation to the relation [7]
1/Tlla = aADWPT ° ~-~'"
(2)
Typically, 1 ~< ~ < 2 and 0.5 ~< 7a ~< 1.5 [2]. The second contribution 1/Tllb is caused by diffusive motions of the F - and Li + ions, and is given for slow ionic motion (ogr>>1) by the expression 1/Txlb oZ t~ ~'bexp( -- ENsR/kT).
(3)
Evaluation of the data leads to ENSR= 0.43 eV which corresponds to an exponent /3= ENSR/ E~ = 0.52 in the KWW function using 0.83 eV for the activation energy, E,, of the dc conductivity [8]. The observed value of/3 agrees well with those obtained in other inorganic glasses [8]. Further, the coupling theory [8] predicts 7b 1 + / 3 ~ 1.5. By contrast with the NSR data in ZBLALi, the NSR data of the CLAP glass have to be interpreted =
Fig. 2. Temperature dependence of 19F NSR rates in CLAP glass and ZBLALi glass measured at 23.31 and 56.38 MHz in the laboratory frame ( l / T , ) and at 52 kHz in the rotating frame (1/Tip).
in terms of three different contributions:
1/TI = 1/TI]a + 1/Tllb + 1/Tl]c.
(4)
The first term is caused by the same process as presented in Eq. (1). The parameters, however, differ remarkably from the corresponding parameters of the Z r - F glass. We found, in the entire temperature range, ~ = 0, indicating a type of 'saturation' effect typical for an LFE-induced NSR process at higher temperatures [6]. We propose that starts to increase with decreasing temperatures below room temperature. Further, the data yield 7a~0.5 indicating a very weak frequency dependence of the LFE-induced NSR rate. The ratio aADwp(CLAP)/ aADwP(ZBLALi) was found to be about 20, demonstrating that extremely strong fluctuations of a large number of ADWP configurations exist in CLAP glasses. Since these fluctuations are not observed by conductivity measurements [1], one has to conclude that the underlying process is of magnetic origin due to movements of 19F nuclear probes without accompanying charge fluctuations. The second contribution, 1/T1]b, was found to
1376
R. Kiichler et al. / Journal of Non-Crystalline Solids 172-174 (1994) 1373-1377
obey formally Eq. (3). However, the observed value of 0.11 eV for ENSR is very small compared with E, = 1.1 eV measured by Moynihan et al. [1], which indicates that the underlying NSR mechanism is not caused by a diffusive ionic motion. For a diffusion-induced process, one would expect ENSR~0.5 E, in accord with the coupling model [8]. We assume that the observed NSR process is due to another type of ADWP configuration related to the dynamics of fluorine atoms, i.e., a hindered rotational motion of a fraction of F--ions. It is known that the corresponding activation energies of rotational motions in solids are of the order of 0.1 eV [9]. Further, from the data we obtained 7b--0.9 for the frequency exponent in Eq. (3). The third contribution, 1/T~I¢, becomes significant above Tg. We found that the T~ data in the MHz-regime (Zeeman relaxation) can be evaluated well by means of the BPP relation ~ 1l ¢ = ( ~ ° ~ i P )
[% 4 % 21 2 • 1 -2 2 + + COo% 1 + 4O9o%
(5)
Analysis of the data yields (~O2ip) = 4.5 x 109 s -2 for the strength of the magnetic dipole interaction and zc = 2.7x 10 -21 exp(1.6 eV/kT)s for the correlation time.
perature range. This good correspondence supports the interpretation that R,~ 1 in the 56 MHz region. Additional 7"1 measurements at lower frequencies are planned in order to test this proposal more carefully. On the other hand, the Tip data in the kHz regime deviate greatly from the BPP behavior. This large deviation is likely to be caused by a combination of the decoupling of the structural and conductivity relaxations and the increased nonexponentiality (possibly T-dependent) of both now decoupled relaxation processes as T is lowered towards Tg. The temperature at which the 1/T~p data peak for 52 kHz is significantly higher than the temperature at which the electric loss modulus would peak at the same frequency as inferred from the data of Moynihan [1]. Therefore the peak in 1/T~p is identified with the structural relaxation. Moreover, a comparison with electric modulus data confirms that R, has become >>1 or the structural relaxation has decoupled from the conductivity relaxation in the lower frequency region. This behavior is again analogous to CKN. A separate peak due to diffusive F - motion corresponding to the decoupled conductivity relaxation is not detected in our T~p data. One possible reason for this is the uncommonly strong ADWP contri-
3. D i s c u s s i o n s T [K]
Fig. 3 shows a fit to the Tt data measured at 56.38 MHz by means of Eqs (2)-(5) using the parameters given in the text. The figure demonstrates the quality of the fit procedure by means of the three different contributions (a)-(c). From the symmetric shape of the NSR rate peak, one has to conclude that the KWW exponent fl ~ 1 in the high temperature region corresponding to 56 MHz. This conclusion in turn suggests that the structural and conductivity relaxations are fully coupled to each other (i.e., R, ~ 1) and the stretch exponent of structural relaxation at these high temperatures has already reached the value of 1. Such a behavior has already been seen in CKN, albeit the fl,~ 1 regime was attained only at the GHz region [10,5]. The magnitude of the correlation time, zo, agrees well with the conductivity relaxation time obtained by Moynihan from dc conductivity data in this tern-
102
800 ,
600 500 ~: : ,
400 ,
300 ,
T• w
!i~
':
• CLAP 56.38 MHz
1 01
6 100
/
ell
t.
1.0
1.5
2.0
2.5
3.0
3.5
1/T [10-a K-1 ]
Fig. 3. Fit of NSR rate 1/T1 in CLAP glass consisting of the three different contributions (a)-(c).
R. Kiichler et al. / Journal o['Non-Crystalline Solids" 172-174 (1994) 1373 1377
bution to NSR in the CLAP glasses (processes a and b) which covers the peak due to F- diffusion. The unusual asymmetric shape of the 1/Tip peak is probably caused by the Vogel-Fulcher temperature dependence of the structural relaxation time which is stronger at lower temperatures, particularly approaching Tg, and a much weaker temperature dependence at high temperatures. In summary, the exact origin of the NSR rate peak observed at 52 kHz (rotating frame relaxation) is not fully understood. Generally, because of the low-frequency observation 'window', the underlying relaxation mechanism has to be slow compared with zs given above. Hence, a structural relaxation (~) process which slows down for temperatures approaching Tg could be responsible for the NSR rate peak. The unusual asymmetry of the peak could be caused by two (or more) different processes with comparable correlation times. Further Tip experiments are in progress in order to obtain more detailed experimental information.
4. Conclusions F i r s t 19F NSR measurements have been carried out for CLAP fluoride glasses between room temperature and 800 K in the kHz and MHz region. The NSR rates are interpreted in terms of three contributions. Two contributions (a,b) are assumed to be caused by the dynamics of different network fluctuations exhibiting the following temperature and frequency dependences: l/T1[ a ~ w -°'5, independent of T; 1/Tllb vc to-°9exp( -- 0.1 eV/kT). The findings are in accord with proposals of the ADWP model mostly used to describe the lowfrequency excitations of network configurations related to the disorder state. In particular, the observed weak frequency and temperature dependence of the NSR rate is confirmed by the ADWP model. The third contribution (c) which becomes significant above Tg shows a maximum around 700 K. Evaluation of the data in the MHz region leads to a correlation time zc = 2.7 x 10 21 exp(1.6 eV/kT)(s) for the underlying NSR process.
1377
We propose that the process is due to the coupled structural relaxation and diffusive motion of F ions in accord with results of conductivity experiments performed by Moynihan and co-workers. The symmetry of the NSR rate peak indicates a Debye-like relaxation, i.e., a KWW exponent f l - 1 at temperatures far above Tg. By contrast, the underlying dynamics of the asymmetric NSR rate peak measured in the kHz range are due to the structural relaxation which has decoupled from the F- ion motion. The corresponding slow correlation time of about 10-6s indicates that a structural relaxation process is responsible for the observed NSR rate peak. Further, the observed asymmetry of the peak can be caused by the Vogel-Fulcher temperature dependence of the structural relaxation time. Further NSR experiments are in progress to elucidate the unknown relaxation mechanisms. The authors would like to thank Professor C.T. Moynihan and Professor C.A. Angell for fruitful discussions. Further, they are grateful to Professor Moynihan for providing the CLAP glasses and conductivity data in these glasses prior to publication. References
[1] C.T. Moynihan, presented at this Meeting. [2] F.S. Howell, R.A. Bose, P.B. Macedo and C.T. Moynihan, J. Phys. Chem. 78 (1974) 639. [3] K.L. Ngai, Solid State Ionics 5 (1981) 27. [4] K.L. Ngai and J. Mundy, in: The Physics of Non-Crystalline Solids, ed. L.D. Pye, W.C. La Course and H.J. Stevens (Taylor and Francis, London 1992) p. 342. [5] K.L:. Ngai, in: Non-Debye Relaxations in Condensed Matter, ed. T.V. Ramakrishnan (World Scientific, Singapore, 1987) p. 23. [6] O. Kanert, J. Steinert, H. Jain and K.L. Ngai, J. NonCryst. Solids 131-133 (1991) 1001. [7] G. Balzer-J611enbeck, O. Kanert, J. Steinert and H. Jain, Solid State Commun. 65 (1988) 303. [8] G. Balzer-J611enbeck, O. Kanert, H. Jain and K.L. Ngai, Phys. Rev. B39 (1989) 6071. [9] I. Svare, G. Thorkildsen and K. Otnes, J. Phys. C12 (1979) 2177. [10] C.A. Angell and L. Torell, J. Chem. Phys. 78 (1983) 937.
Journal of Non-Crystalline Solids 172-174 (1994) 1373-1377
ELSEVIER
Study of nuclear spin relaxation in CLAP glasses R. K f i c h l e r a, O . K a n e r t a, M . F r i c k e a, H . J a i n b, K . L . N g a i c'* a Institute of Physics, University of Dortmund, Dortmund, German)' b LeHigh University, Bethlehem, PA, USA c Naval Research Laboratory, Code 6807, Washington, DC 20375-5000, USA
Abstract
19F nuclear spin relaxation (NSR) rates are reported at various frequencies between room temperature and about 800 K, i.e., below and above the glass transition temperature, T~_-__570K, for glasses of the general composition CdF2-LiF-A1F3 PbF2 (CLAP glasses). The observed NSR rate comes from three different contributions. These contributions are related to degrees of freedom of the F- ions, and are compared with conductivity data performed by Moynihan and co-workers on the same glass.
1. Introduction
Recent conductivity experiments carried out by Moynihan and co-workers show an uncommon decrease of the exponent fl of the KohlrauschWilliams-Watts (KWW) function ~(t) = e x p [ - (t/z) ~] with increasing temperature above the glass transition temperature, Tg, in CLAP glasses [1]. This unusual temperature dependence of fl has been seen before only in the glass-forming molten salt 0.4Ca(NO3)2-0.6KNO3 (CKN) above its glass transition temperature [2,3]. In view of the drastic difference in chemical composition of these two glass-forming ionic materials, this unusual behavior being commonly shared by them is interesting and it warrants further investigation. Such further investigations may eventually lead us to a bet-
* Corresponding author. Tel: + 1-2027676150. Telefax: + 1202 7670546.
ter understanding of the dynamics of diffusion of ions in them. The anomalous behavior of fl in C K N has remained unexplained until a recent attempt in the framework of the coupling model [4]. The key observation in this explanation is that R , ( T ) = (rs(T))/(%(T)), defined as the ratio of the average structural relaxation time, (%(T)), to the average conductivity relaxation time, (%(T)), at T - - Tg is only about 104 in C K N (compared with 101°-10 ~4 in alkali silicate glasses and fast ionic conductors). Further, when T is increased above Tg, Re(T) decreases towards 1. Thus, there is a temperature region above Tg in C K N where a broad crossover from coupled to decoupled structural and conductivity relaxations occur. At sufficiently high temperature above T~ when Re is close to 1, structural relaxation and conductivity relaxation are fully coupled together. Non-exponentiality of the structural relaxation as described by the stretch exponent, fl(T), of the KWW structural relaxation function is determined by the cooperative rearrangement dynamics of basic structural units.
0022-3093/94/$07.00 © 1994 ElsevierScience B.V. All rights reserved SSDI 0 0 2 2 - 3 0 9 3 ( 9 4 ) 0 0 0 5 1 - N
1374
R. Kiichler et al. / Journal of Non-Crystalline Solids 172-174 (1994) 1373-1377
Since the structural relaxation and conductivity relaxation are fully coupled, i.e., R d T ) ~ I , the stretch exponent fl~(T) of conductivity relaxation becomes the same as fls(T) of structural relaxation. For CKN, the condition Re ~ 1 holds at high temperatures and remains approximately valid down to T ~ 100°C at which from mechanical measurements fls = 0.52 and fl~ = 0.48 from conductivity relaxation measurements [5]. The two stretch exponents are essentially equal as expected because their common origin is the cooperative dynamics of structural relaxation. On further decrease of T below 100°C towards Tg, Re(T) starts to increase rapidly to reach 104 at T = Tg, indicating that at the same time the conductivity relaxation is also increasingly decoupled from the structural relaxation. When the conductivity relaxation is totally decoupled from the structural relaxation (i.e., when R,>>I), its non-exponentiality or fl~ is no longer determined by the cooperative coupled dynamics of structural relaxation but now instead by the interactions between the ions and counterions in the molten salt. It can be safely assumed that this change in mechanism is realized at T = Tg when R ~ 1 0 4 and the experimentally found value of ft,(Tg) = 0.74 can be defined with the stretch exponent caused by mutual interactions between the ions alone in CKN. Thus, as the melt is cooled from about 150°C down to Tg, the origin of fl~ starts from being purely structural relaxation dynamics which has a stretch exponent of 0.52, then shifts gradually to being a mixture of both mechanisms, and finally to being entirely due to interactions between the ions which has the value of 0.72 for CKN. As a consequence, ft, has to exhibit the anomalous increase with decreasing temperature as
observed in CKN. It would be interesting to see if this explanation holds also for CLAP glasses. The fact that CLAP glasses also have comparable values of decoupling index, Rd T), at Tg and similar temperature dependence is an encouraging sign for such a possibility. In general conductivity data can be better understood when complemented by nuclear spin relaxation (NSR) measurements. In order to obtain further information about the subject, we have performed 19F NSR measurements between room temperature and about 800 K on a CLAP glass of the same composition as used for the conductivity experiments. For comparison, we have carried out a d d i t i o n a l 19F NSR experiments on a fluorozirconate glass in the same temperature range. The exact compositions of the two glasses are listed in Table 1. It has to be remarked that the 19F nuclear probe has a spin I = 1/2, i.e., the observed NSR rates are caused by fluctuations of nuclear magnetic dipole-dipole interactions between the 19F probes (I-! interaction) and between the ~9F probes and other magnetic species in the sample such as 2TA1, VLi, etc. (I-S interaction). To the contrary, because of the missing nuclear quadrupole moment of 19F, fluctuations of electric field gradients due to moving charges do not contribute to the NSR process. As shown in Fig. 1, the time evolution of the 19F nuclear magnetization in the laboratory frame (Zeeman relaxation T1) as well as in the rotating frame (rotating frame relaxation T~p) obeys an exponential law to a good approximation. From the slopes of the decay, the corresponding NSR rates 1/T~ and 1/T~p, respectively, were calculated.
2. Experimental results
Table 1 Properties of glasses investigated Sample
Composition (mol%)
Tg (K)
T¢,y~tal(K)
CLAP
9.5CDF2-11.5CdO -3CdC12-6LiF-4KF -30AIFa-30PbF2-4YF3 -2LaF3
500580
770
ZBLALi
48ZrF4-22BaF2 -5LaF3-4A1F3-21 LiF
528
630
Fig. 2 exhibits the temperature dependence of the 19F NSR rates in the CLAP glass observed at three different frequencies. Further, for comparison the figure shows ~9FNSR data in the ZBLALi glass measured at 56.38 MHz. Obviously, the CLAP data differ remarkably from the NSR data in ZBLALi. The latter can be interpreted in terms of a common approach used for various oxide and
R. Kiichler et al. / Journal o f Non-Crystalline Solids 172 174 (1994) 1373-1377 I
i
~T
i
i
336K
=
T[K] 800
600
=m= v
O.
N"
=
1 02
1375
496. m s
500
400
300
% lie
1 03
=~=.=
E
l= l= •
tO
• =•
¢-
I
T1 p= 6 . 5 4 m~
1 01
1 01
•
"
°
~
*e
• •0°
o
I
I
'i '
time [arb. units]
o o e •
o o • •
ZBLALi •
i
',Tg
•
A A •
56.38 MHz
• " • • A • ~,
i
1 0 "1 I
1.0
o(~eo
•
,
Fig. 1. Decay of 19F nuclear magnetization in the laboratory frame, mz(t), and in the rotating frame, rap(t), for CLAP glass. Decays are exponential in the measured temperature region.
•
i
I 00
I
56.38 MHz
oo
eo oo•O ~e%eeoeJeeeee e i •
I
•
CLAP • 52 kHz o 23.31 MHz
o ,Do • ".o II o ,
O'l
E
=
Tg
1 02
N
1.5
i
• I
I
I
2.0
2.5
3.0
3.5
1 / T [1 0 .3 K 1 ]
Z r - F glasses [6]:
(1)
1/T1 = l/Tlla + 1/Tllb.
Here, 1/Tll, denotes a low-temperature NSR process due to low-frequency excitations (LFE) of disorder modes intrinsic to the glassy state of matter. The process is commonly described by the asymmetric double-well potential (ADWP) model leading in first approximation to the relation [7]
1/Tlla = aADWPT ° ~-~'"
(2)
Typically, 1 ~< ~ < 2 and 0.5 ~< 7a ~< 1.5 [2]. The second contribution 1/Tllb is caused by diffusive motions of the F - and Li + ions, and is given for slow ionic motion (ogr>>1) by the expression 1/Txlb oZ t~ ~'bexp( -- ENsR/kT).
(3)
Evaluation of the data leads to ENSR= 0.43 eV which corresponds to an exponent /3= ENSR/ E~ = 0.52 in the KWW function using 0.83 eV for the activation energy, E,, of the dc conductivity [8]. The observed value of/3 agrees well with those obtained in other inorganic glasses [8]. Further, the coupling theory [8] predicts 7b 1 + / 3 ~ 1.5. By contrast with the NSR data in ZBLALi, the NSR data of the CLAP glass have to be interpreted =
Fig. 2. Temperature dependence of 19F NSR rates in CLAP glass and ZBLALi glass measured at 23.31 and 56.38 MHz in the laboratory frame ( l / T , ) and at 52 kHz in the rotating frame (1/Tip).
in terms of three different contributions:
1/TI = 1/TI]a + 1/Tllb + 1/Tl]c.
(4)
The first term is caused by the same process as presented in Eq. (1). The parameters, however, differ remarkably from the corresponding parameters of the Z r - F glass. We found, in the entire temperature range, ~ = 0, indicating a type of 'saturation' effect typical for an LFE-induced NSR process at higher temperatures [6]. We propose that starts to increase with decreasing temperatures below room temperature. Further, the data yield 7a~0.5 indicating a very weak frequency dependence of the LFE-induced NSR rate. The ratio aADwp(CLAP)/ aADwP(ZBLALi) was found to be about 20, demonstrating that extremely strong fluctuations of a large number of ADWP configurations exist in CLAP glasses. Since these fluctuations are not observed by conductivity measurements [1], one has to conclude that the underlying process is of magnetic origin due to movements of 19F nuclear probes without accompanying charge fluctuations. The second contribution, 1/T1]b, was found to
1376
R. Kiichler et al. / Journal of Non-Crystalline Solids 172-174 (1994) 1373-1377
obey formally Eq. (3). However, the observed value of 0.11 eV for ENSR is very small compared with E, = 1.1 eV measured by Moynihan et al. [1], which indicates that the underlying NSR mechanism is not caused by a diffusive ionic motion. For a diffusion-induced process, one would expect ENSR~0.5 E, in accord with the coupling model [8]. We assume that the observed NSR process is due to another type of ADWP configuration related to the dynamics of fluorine atoms, i.e., a hindered rotational motion of a fraction of F--ions. It is known that the corresponding activation energies of rotational motions in solids are of the order of 0.1 eV [9]. Further, from the data we obtained 7b--0.9 for the frequency exponent in Eq. (3). The third contribution, 1/T~I¢, becomes significant above Tg. We found that the T~ data in the MHz-regime (Zeeman relaxation) can be evaluated well by means of the BPP relation ~ 1l ¢ = ( ~ ° ~ i P )
[% 4 % 21 2 • 1 -2 2 + + COo% 1 + 4O9o%
(5)
Analysis of the data yields (~O2ip) = 4.5 x 109 s -2 for the strength of the magnetic dipole interaction and zc = 2.7x 10 -21 exp(1.6 eV/kT)s for the correlation time.
perature range. This good correspondence supports the interpretation that R,~ 1 in the 56 MHz region. Additional 7"1 measurements at lower frequencies are planned in order to test this proposal more carefully. On the other hand, the Tip data in the kHz regime deviate greatly from the BPP behavior. This large deviation is likely to be caused by a combination of the decoupling of the structural and conductivity relaxations and the increased nonexponentiality (possibly T-dependent) of both now decoupled relaxation processes as T is lowered towards Tg. The temperature at which the 1/T~p data peak for 52 kHz is significantly higher than the temperature at which the electric loss modulus would peak at the same frequency as inferred from the data of Moynihan [1]. Therefore the peak in 1/T~p is identified with the structural relaxation. Moreover, a comparison with electric modulus data confirms that R, has become >>1 or the structural relaxation has decoupled from the conductivity relaxation in the lower frequency region. This behavior is again analogous to CKN. A separate peak due to diffusive F - motion corresponding to the decoupled conductivity relaxation is not detected in our T~p data. One possible reason for this is the uncommonly strong ADWP contri-
3. D i s c u s s i o n s T [K]
Fig. 3 shows a fit to the Tt data measured at 56.38 MHz by means of Eqs (2)-(5) using the parameters given in the text. The figure demonstrates the quality of the fit procedure by means of the three different contributions (a)-(c). From the symmetric shape of the NSR rate peak, one has to conclude that the KWW exponent fl ~ 1 in the high temperature region corresponding to 56 MHz. This conclusion in turn suggests that the structural and conductivity relaxations are fully coupled to each other (i.e., R, ~ 1) and the stretch exponent of structural relaxation at these high temperatures has already reached the value of 1. Such a behavior has already been seen in CKN, albeit the fl,~ 1 regime was attained only at the GHz region [10,5]. The magnitude of the correlation time, zo, agrees well with the conductivity relaxation time obtained by Moynihan from dc conductivity data in this tern-
102
800 ,
600 500 ~: : ,
400 ,
300 ,
T• w
!i~
':
• CLAP 56.38 MHz
1 01
6 100
/
ell
t.
1.0
1.5
2.0
2.5
3.0
3.5
1/T [10-a K-1 ]
Fig. 3. Fit of NSR rate 1/T1 in CLAP glass consisting of the three different contributions (a)-(c).
R. Kiichler et al. / Journal o['Non-Crystalline Solids" 172-174 (1994) 1373 1377
bution to NSR in the CLAP glasses (processes a and b) which covers the peak due to F- diffusion. The unusual asymmetric shape of the 1/Tip peak is probably caused by the Vogel-Fulcher temperature dependence of the structural relaxation time which is stronger at lower temperatures, particularly approaching Tg, and a much weaker temperature dependence at high temperatures. In summary, the exact origin of the NSR rate peak observed at 52 kHz (rotating frame relaxation) is not fully understood. Generally, because of the low-frequency observation 'window', the underlying relaxation mechanism has to be slow compared with zs given above. Hence, a structural relaxation (~) process which slows down for temperatures approaching Tg could be responsible for the NSR rate peak. The unusual asymmetry of the peak could be caused by two (or more) different processes with comparable correlation times. Further Tip experiments are in progress in order to obtain more detailed experimental information.
4. Conclusions F i r s t 19F NSR measurements have been carried out for CLAP fluoride glasses between room temperature and 800 K in the kHz and MHz region. The NSR rates are interpreted in terms of three contributions. Two contributions (a,b) are assumed to be caused by the dynamics of different network fluctuations exhibiting the following temperature and frequency dependences: l/T1[ a ~ w -°'5, independent of T; 1/Tllb vc to-°9exp( -- 0.1 eV/kT). The findings are in accord with proposals of the ADWP model mostly used to describe the lowfrequency excitations of network configurations related to the disorder state. In particular, the observed weak frequency and temperature dependence of the NSR rate is confirmed by the ADWP model. The third contribution (c) which becomes significant above Tg shows a maximum around 700 K. Evaluation of the data in the MHz region leads to a correlation time zc = 2.7 x 10 21 exp(1.6 eV/kT)(s) for the underlying NSR process.
1377
We propose that the process is due to the coupled structural relaxation and diffusive motion of F ions in accord with results of conductivity experiments performed by Moynihan and co-workers. The symmetry of the NSR rate peak indicates a Debye-like relaxation, i.e., a KWW exponent f l - 1 at temperatures far above Tg. By contrast, the underlying dynamics of the asymmetric NSR rate peak measured in the kHz range are due to the structural relaxation which has decoupled from the F- ion motion. The corresponding slow correlation time of about 10-6s indicates that a structural relaxation process is responsible for the observed NSR rate peak. Further, the observed asymmetry of the peak can be caused by the Vogel-Fulcher temperature dependence of the structural relaxation time. Further NSR experiments are in progress to elucidate the unknown relaxation mechanisms. The authors would like to thank Professor C.T. Moynihan and Professor C.A. Angell for fruitful discussions. Further, they are grateful to Professor Moynihan for providing the CLAP glasses and conductivity data in these glasses prior to publication. References
[1] C.T. Moynihan, presented at this Meeting. [2] F.S. Howell, R.A. Bose, P.B. Macedo and C.T. Moynihan, J. Phys. Chem. 78 (1974) 639. [3] K.L. Ngai, Solid State Ionics 5 (1981) 27. [4] K.L. Ngai and J. Mundy, in: The Physics of Non-Crystalline Solids, ed. L.D. Pye, W.C. La Course and H.J. Stevens (Taylor and Francis, London 1992) p. 342. [5] K.L:. Ngai, in: Non-Debye Relaxations in Condensed Matter, ed. T.V. Ramakrishnan (World Scientific, Singapore, 1987) p. 23. [6] O. Kanert, J. Steinert, H. Jain and K.L. Ngai, J. NonCryst. Solids 131-133 (1991) 1001. [7] G. Balzer-J611enbeck, O. Kanert, J. Steinert and H. Jain, Solid State Commun. 65 (1988) 303. [8] G. Balzer-J611enbeck, O. Kanert, H. Jain and K.L. Ngai, Phys. Rev. B39 (1989) 6071. [9] I. Svare, G. Thorkildsen and K. Otnes, J. Phys. C12 (1979) 2177. [10] C.A. Angell and L. Torell, J. Chem. Phys. 78 (1983) 937.