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NMR relaxation at pressures up to 7 kbar in the superionic conductor Ag3SBr
Physica 139 & 140B (1986) 289-291 North-Holland, Amsterdam
NMR RELAXATION AT PRESSURES UP TO 7 kbar IN THE SUPERIONIC CONDUCTOR AgaSBr
H. H U B E R , M. MALl, J. ROOS and D. BRINKMANN Physik-lnstitut der Universitdt Ziirich, 8001 Ziirich, Switzerland
NMR studies of Br and Ag nuclei in the superionic conductor Ag3SBr at pressures up to 7 kbar have been performed. The obtained phase diagram shows a linear increase of the/3-7 transition temperature with rising pressure. The temperature dependence of the Ag-spin-lattice relaxation at constant pressure is analyzed in terms of two thermally activated contributions related to the Ag-ion diffusional jumps. The extracted activation energies at 1 bar are in agreement with conductivity measurements. Pressure dependent relaxation yield negative activation volumes amounting to (-7.5-+ 1.2) cm3/mol at 6 kbar.
1. Experimental
Powder samples of Ag3SBr were prepared out of solution following the procedure given by Kennedy and Chen [1]. The high pressure NMR investigations were performed in a berylliumcopper vessel, details are given in ref. [2].
however, the Br signal disappears gradually within a range of 1 kbar. For convenience we assigned the transition pressure to the point where the line intensity is half of its original value. The variation of the transition temperature with pressure is found to be linear up to 7kbar: T c ( p ) = To(1 bar) + ap, a = (5.7 - 0.4) × 10 -3 K/bar.
2.2. Ag-relaxation 2. Results
2.1. Phase diagram Ag3SBr is known to exist in two phases at normal pressure [3,4]. The low conducting Tphase is orthorhombic (spacegroup D2h ~7) and transforms through a first order phase transition at 128 K into the superionic cubic/3-phase (spacegroup 0~h) which is stable up to the decomposition temperature of 703 K. We studied the/3-T-transition temperature T c (fig. 1) observing the S~Br resonance in a field of 5.17T. Because of the point symmetry m3m of the bromine site in the /3-phase there is no static quadrupolar interaction and a single resonance line is observed. In the y-phase the Br site symmetry changes to mm, leading to orientation dependent quadrupole interactions. Therefore in our powder sample the Br signal excessively broadens and becomes undetectable. Inducing the/3-y-phase transition at constant temperature by increasing pressure,
Measurements of both the Ag- and Br-relaxation were performed in order to study the diff-
190
Ag3SBr
180 170
S
~- 160
150 140 13( 12( Plkbarl
Fig. 1. Pressure dependence of the /3-T-phase transition in Ag3SBr determined by 81Br NMR.
0378-4363/86/$03.50 (~ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
290
H. Huber et al. / N M R relaxation up to 7 kbar in Ag~SBr i
i
i
i
,
I
,
,
2
4
(5
8
r--1 I-..~
__x
10-1
Ii
1OOO [K-I] T Fig. 2. Relaxation rate of l°9mgin Ag3SBr at 5.17T and two different pressures. The lines are computer fits according to the two-process model. The respective/3-T-transition temperatures are indicated. usion phenomena as seen by the stationary Brions [5] and as experienced by the mobile Agions. In this paper we present the Ag-measurements. Fig. 2 shows the temperature dependence of the Ag spin-lattice relaxation rate 1 / T~ at 1 bar and at 7 kbar. The observation is restricted to the /3-phase. No measurements were made in the low conducting y-phase because the relaxation time becomes prohibitively long. The upper temperature limit of the 7 k b a r data is given by the decreasing tensile strength of Berylco 25 for lITI
109Ag in Ag3SBr
Is-l]
T=335K
I \ \
\\ \
\
/
\\ \/
_T:_23B.K. . . .
"
temperatures above 350 K. The important features of the normal pressure curve are a pronounced maximum at 312 K and a thermally activated behavior with apparent activation energies of 0.31 eV on its high temperature side and 0.11 eV and 0.05 eV o'n its low temperature side. The 7 k b a r data show a shift of the maximum down to 270 K and a change of the low temperture slope. Detailed studies of the pressure dependence of the rate on both sides of the normal pressure maximum are shown in fig. 3. The data are tentatively described by a power law dependence of the form 1 / T l ( p ) - l / T ~ ( l b a r ) = _ _ _ a p 4 (a = (8--- 1) × 10 -16 s -l bar-4). The high temperature rate is found to decrease with pressure whereas the low temperature rate increases.
3. Discussion Superionic properties are normally due to the existence of several regular or interstitial lattice sites available for every mobile ion. For an Agion in/3-Ag3SBr there are 4(h)-sites located close to the center of the cube faces. Similar to the compound/3-Ag3SI [61 and as estabished by our measurements of the 8 Br linewidth [5] there is a potential barrier height of about 0.03 eV between these neighbouring sites. However, the distance between these positions is much less than the Ag ionic radius, so usually only one Ag-site is occupied at a time. The structure allows for two different kinds of motions: local jumps between the 4 A g sites within a cube face and diffusional jumps between neighbouring faces. From these only the latter contribute to the dc-conductivity [7]. To explain the data quantitatively we propose the following form for the Ag relaxation rate: I/T 1 =
(AIOOL)2
'rl 1 + (O)LTI) 2
r2
pressure[ kbarl Fig. 3. Pressure d e p e n d e n t relaxation rates of "~Ag in Ag~SBr at two t e m p e r a t u r e s . D a s h e d lines represent the +_a p L b e h a v i o r .
q- ( A 2 0 ) L ) 2
1 q- (O)LT2) 1"33 "
The rate consists of two contributions based on the same nuclear spin interaction. Though not
H. Huber et al. / NMR relaxation up to 7 kbar in Ag3SBr
shown here we also measured the frequency dependence of the normal pressure rates. They decrease with decreasing Larmor frequency toL indicating anisotropic chemical shift relaxation taken into account by the factors Aito L (i = 1, 2). The first term (contribution 1) dominates for temperatures above 250 K where single particle hopping into neighbouring vacant cube faces accounts for the observed high temperature maximum. At lower temperatures the second term (contribution 2) displaying the effect of increasing ion-ion correlations becomes dominant. In contribution 1 the Ag hopping rate 1 / z I is closely related to the temperature dependent vacancy concentration c ( T ) = c o + c o e x p ( - E f / k T ) . Here c o -- 1% is the temperature independent concentration whereas the second term describes the thermally activated formation of vacancies. Since significant under-occupation of the regular /3phase Ag positions of about 4% is known to be present in Ag3SI [8] the assumed small concentration of Ag vacancies not yet detected by X-rays in Ag3SBr is justified. One therefore has for the Ag hopping rate 1/~-~ = 1 / % - c ( T ) where 1/% = 1/%0 e x p ( - E m l / k T ) is the vacancy hopping rate. This non-simple Arrhenius behavior is responsible for the asymmetry in the high and low temperature slopes on both sides of the maximum. The activation energies for formation and migration extracted from our data analysis are 0.19eV and 0.13 eV, respectively, in fairly good agreement with the double exponential dc-conductivity behavior above 160 K reported by Magistris et al. (0.22 eV and 0.10 eV) [9]. In contribution 2 the Ag hopping rate 1/r 2 = 1/r20 e x p ( - E m 2 / k T ) is thermally activated as well but with a slightly higher migration energy Em2 = 0.14 eV in accord with conductivity measurements [9]. In contrast to contribution 1 we find significant deviation from the BPP-type frequency behavior as can be seen from the exponent 1.33 ( B P P - e x p o n e n t = 2) [10]. The non-BPP relaxation behavior, often found in superionics [11] indicates that correlations between the ions become important at lower temperatures leading to a weaker than exponential decay of the correlation functions. Using the proposed form for 1 / T~ a fit to the 7 kbar data is obtained just by lowering
291
the migration energy Eml from 0.13 eV at 1 bar to 0.11 eV at 7 kbar keeping the other parameters unchanged. This seems to be a reasonable result since it physically describes the effect of crystal compression in terms of reduction of migration barrier height. A decrease of migration energy should result in an increase of the dc-conductivity in the /3-phase implying a negative activation volume AVm = (tgEm/Op)r" AVm can tentatively be calculated from the pressure dependence of the relaxation rate (fig. 3). The calculated values are negative and decrease with pressure reaching ( - 7 . 5 - 1.2) cm3/mol at 6 kbar. For pressures below 2 kbar a good agreement with values reported by Hoshino et al. [12] ( - 0 . 5 cm3/mol at 333 K) is obtained. In order to test these findings conductivity data at higher pressures up to 7 kbar are needed.
Acknowledgements This work was supported in part by the Swiss National Science Foundation.
References [1] J.H. Kennedy and F. Chen, J. Electrochem. Soc. 116 (1969) 207. [2] H. Huber, M. Mali, J. Roos and D. Brinkmann, Rev. Sci. Instr. 55 (1984) 1325. [3] T. Sakuma and S. Hoshino, J. Phys. Soc. Japan 49 (1980) 678. [4] A. Magistris, G. Chiodelli and A. Schiraldi, Zeitschr. Phys. Chem. Neue Folge 112 (1978) 251. [5] H. Huber, M. Mali, J. Roos and D. Brinkmann, Helv. Phys. Acta 57 (1984) 738. [6] E. Perenthaler and H. Schulz, Sol. Stat. Ion. 2 (1981) 43. [7] P. Bruesch, H.U. Beyeler and S. Strfissler, Phys. Rev. B25 (1982) 541. [8] E. Perenthaler, H. Schulzand H.W. Beyeler, Acta Cryst. B37 (1981) 1017. [9] G. Chiodelli, A. Magistris and A. Schiraldi, Zeitschr. Phys. Chem. Neue Folge 118 (1979) 177. [10] N. Bloembergen, R.V. Pound and E.M. Purcell, Phys. Rev. 73 (1948) 679. [11] J.L. Bjorkstam and M. Villa, Magn. Res. Rev. 6 (1980) 1. [12] H. Hoshino, H. Yanagiyaand M. Shimoji, J. Chem. Soc. Farad. Trans. I 70 (1974) 281.
NMR RELAXATION AT PRESSURES UP TO 7 kbar IN THE SUPERIONIC CONDUCTOR AgaSBr
H. H U B E R , M. MALl, J. ROOS and D. BRINKMANN Physik-lnstitut der Universitdt Ziirich, 8001 Ziirich, Switzerland
NMR studies of Br and Ag nuclei in the superionic conductor Ag3SBr at pressures up to 7 kbar have been performed. The obtained phase diagram shows a linear increase of the/3-7 transition temperature with rising pressure. The temperature dependence of the Ag-spin-lattice relaxation at constant pressure is analyzed in terms of two thermally activated contributions related to the Ag-ion diffusional jumps. The extracted activation energies at 1 bar are in agreement with conductivity measurements. Pressure dependent relaxation yield negative activation volumes amounting to (-7.5-+ 1.2) cm3/mol at 6 kbar.
1. Experimental
Powder samples of Ag3SBr were prepared out of solution following the procedure given by Kennedy and Chen [1]. The high pressure NMR investigations were performed in a berylliumcopper vessel, details are given in ref. [2].
however, the Br signal disappears gradually within a range of 1 kbar. For convenience we assigned the transition pressure to the point where the line intensity is half of its original value. The variation of the transition temperature with pressure is found to be linear up to 7kbar: T c ( p ) = To(1 bar) + ap, a = (5.7 - 0.4) × 10 -3 K/bar.
2.2. Ag-relaxation 2. Results
2.1. Phase diagram Ag3SBr is known to exist in two phases at normal pressure [3,4]. The low conducting Tphase is orthorhombic (spacegroup D2h ~7) and transforms through a first order phase transition at 128 K into the superionic cubic/3-phase (spacegroup 0~h) which is stable up to the decomposition temperature of 703 K. We studied the/3-T-transition temperature T c (fig. 1) observing the S~Br resonance in a field of 5.17T. Because of the point symmetry m3m of the bromine site in the /3-phase there is no static quadrupolar interaction and a single resonance line is observed. In the y-phase the Br site symmetry changes to mm, leading to orientation dependent quadrupole interactions. Therefore in our powder sample the Br signal excessively broadens and becomes undetectable. Inducing the/3-y-phase transition at constant temperature by increasing pressure,
Measurements of both the Ag- and Br-relaxation were performed in order to study the diff-
190
Ag3SBr
180 170
S
~- 160
150 140 13( 12( Plkbarl
Fig. 1. Pressure dependence of the /3-T-phase transition in Ag3SBr determined by 81Br NMR.
0378-4363/86/$03.50 (~ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
290
H. Huber et al. / N M R relaxation up to 7 kbar in Ag~SBr i
i
i
i
,
I
,
,
2
4
(5
8
r--1 I-..~
__x
10-1
Ii
1OOO [K-I] T Fig. 2. Relaxation rate of l°9mgin Ag3SBr at 5.17T and two different pressures. The lines are computer fits according to the two-process model. The respective/3-T-transition temperatures are indicated. usion phenomena as seen by the stationary Brions [5] and as experienced by the mobile Agions. In this paper we present the Ag-measurements. Fig. 2 shows the temperature dependence of the Ag spin-lattice relaxation rate 1 / T~ at 1 bar and at 7 kbar. The observation is restricted to the /3-phase. No measurements were made in the low conducting y-phase because the relaxation time becomes prohibitively long. The upper temperature limit of the 7 k b a r data is given by the decreasing tensile strength of Berylco 25 for lITI
109Ag in Ag3SBr
Is-l]
T=335K
I \ \
\\ \
\
/
\\ \/
_T:_23B.K. . . .
"
temperatures above 350 K. The important features of the normal pressure curve are a pronounced maximum at 312 K and a thermally activated behavior with apparent activation energies of 0.31 eV on its high temperature side and 0.11 eV and 0.05 eV o'n its low temperature side. The 7 k b a r data show a shift of the maximum down to 270 K and a change of the low temperture slope. Detailed studies of the pressure dependence of the rate on both sides of the normal pressure maximum are shown in fig. 3. The data are tentatively described by a power law dependence of the form 1 / T l ( p ) - l / T ~ ( l b a r ) = _ _ _ a p 4 (a = (8--- 1) × 10 -16 s -l bar-4). The high temperature rate is found to decrease with pressure whereas the low temperature rate increases.
3. Discussion Superionic properties are normally due to the existence of several regular or interstitial lattice sites available for every mobile ion. For an Agion in/3-Ag3SBr there are 4(h)-sites located close to the center of the cube faces. Similar to the compound/3-Ag3SI [61 and as estabished by our measurements of the 8 Br linewidth [5] there is a potential barrier height of about 0.03 eV between these neighbouring sites. However, the distance between these positions is much less than the Ag ionic radius, so usually only one Ag-site is occupied at a time. The structure allows for two different kinds of motions: local jumps between the 4 A g sites within a cube face and diffusional jumps between neighbouring faces. From these only the latter contribute to the dc-conductivity [7]. To explain the data quantitatively we propose the following form for the Ag relaxation rate: I/T 1 =
(AIOOL)2
'rl 1 + (O)LTI) 2
r2
pressure[ kbarl Fig. 3. Pressure d e p e n d e n t relaxation rates of "~Ag in Ag~SBr at two t e m p e r a t u r e s . D a s h e d lines represent the +_a p L b e h a v i o r .
q- ( A 2 0 ) L ) 2
1 q- (O)LT2) 1"33 "
The rate consists of two contributions based on the same nuclear spin interaction. Though not
H. Huber et al. / NMR relaxation up to 7 kbar in Ag3SBr
shown here we also measured the frequency dependence of the normal pressure rates. They decrease with decreasing Larmor frequency toL indicating anisotropic chemical shift relaxation taken into account by the factors Aito L (i = 1, 2). The first term (contribution 1) dominates for temperatures above 250 K where single particle hopping into neighbouring vacant cube faces accounts for the observed high temperature maximum. At lower temperatures the second term (contribution 2) displaying the effect of increasing ion-ion correlations becomes dominant. In contribution 1 the Ag hopping rate 1 / z I is closely related to the temperature dependent vacancy concentration c ( T ) = c o + c o e x p ( - E f / k T ) . Here c o -- 1% is the temperature independent concentration whereas the second term describes the thermally activated formation of vacancies. Since significant under-occupation of the regular /3phase Ag positions of about 4% is known to be present in Ag3SI [8] the assumed small concentration of Ag vacancies not yet detected by X-rays in Ag3SBr is justified. One therefore has for the Ag hopping rate 1/~-~ = 1 / % - c ( T ) where 1/% = 1/%0 e x p ( - E m l / k T ) is the vacancy hopping rate. This non-simple Arrhenius behavior is responsible for the asymmetry in the high and low temperature slopes on both sides of the maximum. The activation energies for formation and migration extracted from our data analysis are 0.19eV and 0.13 eV, respectively, in fairly good agreement with the double exponential dc-conductivity behavior above 160 K reported by Magistris et al. (0.22 eV and 0.10 eV) [9]. In contribution 2 the Ag hopping rate 1/r 2 = 1/r20 e x p ( - E m 2 / k T ) is thermally activated as well but with a slightly higher migration energy Em2 = 0.14 eV in accord with conductivity measurements [9]. In contrast to contribution 1 we find significant deviation from the BPP-type frequency behavior as can be seen from the exponent 1.33 ( B P P - e x p o n e n t = 2) [10]. The non-BPP relaxation behavior, often found in superionics [11] indicates that correlations between the ions become important at lower temperatures leading to a weaker than exponential decay of the correlation functions. Using the proposed form for 1 / T~ a fit to the 7 kbar data is obtained just by lowering
291
the migration energy Eml from 0.13 eV at 1 bar to 0.11 eV at 7 kbar keeping the other parameters unchanged. This seems to be a reasonable result since it physically describes the effect of crystal compression in terms of reduction of migration barrier height. A decrease of migration energy should result in an increase of the dc-conductivity in the /3-phase implying a negative activation volume AVm = (tgEm/Op)r" AVm can tentatively be calculated from the pressure dependence of the relaxation rate (fig. 3). The calculated values are negative and decrease with pressure reaching ( - 7 . 5 - 1.2) cm3/mol at 6 kbar. For pressures below 2 kbar a good agreement with values reported by Hoshino et al. [12] ( - 0 . 5 cm3/mol at 333 K) is obtained. In order to test these findings conductivity data at higher pressures up to 7 kbar are needed.
Acknowledgements This work was supported in part by the Swiss National Science Foundation.
References [1] J.H. Kennedy and F. Chen, J. Electrochem. Soc. 116 (1969) 207. [2] H. Huber, M. Mali, J. Roos and D. Brinkmann, Rev. Sci. Instr. 55 (1984) 1325. [3] T. Sakuma and S. Hoshino, J. Phys. Soc. Japan 49 (1980) 678. [4] A. Magistris, G. Chiodelli and A. Schiraldi, Zeitschr. Phys. Chem. Neue Folge 112 (1978) 251. [5] H. Huber, M. Mali, J. Roos and D. Brinkmann, Helv. Phys. Acta 57 (1984) 738. [6] E. Perenthaler and H. Schulz, Sol. Stat. Ion. 2 (1981) 43. [7] P. Bruesch, H.U. Beyeler and S. Strfissler, Phys. Rev. B25 (1982) 541. [8] E. Perenthaler, H. Schulzand H.W. Beyeler, Acta Cryst. B37 (1981) 1017. [9] G. Chiodelli, A. Magistris and A. Schiraldi, Zeitschr. Phys. Chem. Neue Folge 118 (1979) 177. [10] N. Bloembergen, R.V. Pound and E.M. Purcell, Phys. Rev. 73 (1948) 679. [11] J.L. Bjorkstam and M. Villa, Magn. Res. Rev. 6 (1980) 1. [12] H. Hoshino, H. Yanagiyaand M. Shimoji, J. Chem. Soc. Farad. Trans. I 70 (1974) 281.