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7Li and 127I NMR in LiI single crystals
Solid State lonics 28-30 (1988) 1089-1092 North-Holland, Amsterdam
"lLi AND 1271 NMR IN LiI SINGLE CRYSTALS M. MALl, J. ROOS, D. BRINKMANN Physik-lnstitut, Ur,iversitiit Ziirich, 8001 Zurich, Switzerland
J.B. PHIPP~ and P.M. SKARSTAD Medtronic, Inc., Brooklyn Ctr., MN 55430, USA Received 14 August 1987
We have measured tb ."NMR spin-lattice relaxation times of both the stationary 127I and the mobile VLi nuclei in a new single crystal which has been gi own with extreme care in order to keep any impurity content very low. The high temperature relaxation data can consistently be explained by phonon and vacancy diffusion mechanisms. The relevant parameters thus obtained (vacancy concentration as function of temperature with formation energy 1.22 eV and migration energy 0.35 eV, etc.) have been used to predict a Li diffusion coefficient that is in perfect agreement with our previous measurements.
1. Introduction
2. Experimental details
Since the discovery of Liang [ 1 ] that dispersed phase samples of LiI.AI203 showed substantially increased Li conductivity, interest in such materials has greatly increased. In a previous publication [ 2] we have reported NMR studies which aimed to separate features which are characteristic of the bulk from those related to defect and inteffacial effects. We had presented some preliminary results on dispersed phase LiI.SiO2 and LiI.AI203 but had focused attention upon properties of a "'pure" single crystal. During that work it turned out that the single crystal was not of the quality needed for our investigation. The results were puzzling and not fully understood; there were indications that the single crystal was inhomogeneous. Because an understanding of the LiI single crystal properties is a prerequisite for analyzing the data of ~he dispersed phase systems of Lii we have repeated our studies in a new single crystal specimen and have extended them to the re!axation ~f~he ~ ~.ienar-: :;'i nucieL In this paper we report on the first results of these new studies, in particular we will show how the combination of Li and ! data allows us to determine all the relevant parameters such as the number of mobile ions and various activation energies for the Li diffusion.
The single crystals were prepared from LiI obtained from Anderson Physics Laborato~,, Inc., ~Yrbana, IL. The LiI was used as received without further purification. Transfers of material to NMR tubes were carried out quickly in a vacuum atmosphere glovebox filled with helium. Care was taken to minimize exposure of the Li! ~o the atmosphere of ~he glovebox, which was maintained below 100 ppm H20. The free-flowing spheroidal particles of LiI facilitated the transfers and minimized water contamination by having a favorable ratio of surface to volume. The charged NMR tubes were sealed under 0.5 atm He. Single crystals were then grown directly by the Bridgman technique. The crystals were clear throughout; no regrowth or further purification steps were carried out. Single crystals used in earlier experiments [ 2] were grown Lii w'fich had been prepared by dehydration O~P--,~,---~;~ gr~d~ hydrated ~..~ obtained from Alfa Products, Danvers, MA, as described previousi~ [3 ]. In the case of this material, clear material was selected visually from a preliminary growth pass in a larger quartz tube for growth in the NMR tubes. Boules grown subsequently in the NMR tubes appeared on visual inspection to be mainly clear single
0 167-2738/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Paysics Publishing Division)
1090
M. Malt et el.fiLl and t2rl NMR in Lil single crystals
crystals; however, in each case there were significant amounts of polycrystalline white material swept to the top u,"*"~'",:,,,boule, .., which we presume to be lithium oxide. The N M R experiments were performed with a Bruker SPX pulse spectrometer. The 7Li signals were investigated at 2.11 and 0.47 T corresponding to 34.99 and 7.777 MHz, respectively, while the 127I resonance was detected at 2.11 T (18.02 MHz). The spin-lattice relaxation times T~ were measured by either the ,,t-T-it/2 pulse sequence or the 7t/2-T- it/ 2 saturation method. In either case the magnetization recovery was recorded as the free induction decay. When starting with the 7Li relaxation studies we noticed a tremendous dependence of the magnitude of the low temperature Tt values with respect to the position in the single crystal. Sections could be found where T! is up to 40 times larger than values found in the "old" single crystal investigated previously [ 2 ]. Most important, in these sections the Li magnetization recovers exponentially at nearly all temperatures in contrast to a substantial departure from exponential recovery, in our "old" crystal. Simple exponential recovery, is expected for a homogeneous specimen and 1: the absence of quadrupolar splittings. (The cubic symmetry of the Li site leads to zero splitting.) Thus our results prove the better quality of the new single crystal but also its inhomoge:: city. Hence the new specimen was cut into four pieces denoted by A, B, C, and D with "A" and " D " belonging to the ends and "B" and "C" to the center section of the sinEde crystal. These pieces were investigated separately.
3. Iodine and lithium relaxation data The temperature dependence of the t27][relaxation rate in piece "B" has been plotzed in fig. 1. At temperatures where the magnetization recovery was not exponential we have simply plotted the time at which the magnetization had recovered to e- t times its initial value. TI,. 127I relaxation rate data can be fitted by 1/Tt(I)=AT2+Bc(T)[z/(I+co2(I)z2)].
(l)
Both terms describe relaxation arising from thc in-
1 I
i
!
tzrI
\ ' , j o:,o\
""
.elit) t,,,.,=l
i
/6 i , ,~ --
in L i I single crystol v = 18.022MHz
1
\
i--" 10 z "" ~ ' o ~ 0 . . " ~A'°X~o \ 10
i
2
I
3
i
4 1ooo/1
-
810
[K-']
Fig. !. Spin-lattice relaxation rate of 1271at 18.022 MHz in piece "B" of the new single crystal whose 7Li data are given by O in fig. 2. The solid line is a fit ofeq. (1) to the data, the dashed line is an extrapolation of the term AT 2 of eq. (1) to higher temperatures.
teraction of the 1 2 7 I nuclear electric quadrupole moment eQ with fluctuating electric field gradients (EFG). The first term where T is the temperature, describes relaxation due to acoustical lattice vibrations (Raman process). This mechanism dominates relaxation at low temperatures; the extrapolation of its contribution from low to high temperatures is denoted by the dashed line in fig. 1. The second te:'m in eq. (1) which dominates relaxation at high temperatures, arises from the interaction with fluctuating EFG's set up by diffusing defects such as impurities or vacancies. Their concentration c(T) =Co + c ' e x p ( - E f l 2 k T )
(2)
contains a temperature independent extrinsic part Co and a thermally activated intrinsic contribution where Ef is the formation energy, a~(I)/2~ is the 127I Larmor frequency and r is the correlation time of the fluctuating EFG tensor. We identify as usually 1/ r with the mean hopping frequency of the mobile defects, and assume this frequency to be thermally activated: 1/z = (1/Zo) exp( - E m / k T ) ,
(3)
where Em is the migration energy. The steep rise of the rate above 400 K is caused by the increase of the defect concentration. The term co in c(T) is respon-
M. Marl et aL/ZLi and 'Z"lNMR in Lil single crystals
10'
I
l
!
I
I
":~¢ I
I •
I
7Li in LiI single crystals v=34.990MHz
,~'"~'~" .
,A
1
~...
"
""
"
~- 1C/+
First sample
...
-, 0
-a . . . . .
.zx.//,,,_-a- 4x
.. •
.. Q
,.°
'~
-...
10-a _ "'..
,o-3l 1
the inhomogeneity of the specimens and is not relevant to our present problem. The Li relaxation at high temperatures is due to dipolar interaction with fluctuating magnetic fields caused by diffusing defects. We thus describe these data by l/Tt (Li)=Gz(Li)/[ l +to2(Li)r2(Li)] ,
• i.,..=+.e .e.e+.,, ~,
1091
when, we identify the correlation frequency l/r(Li) as the Li ion hopping frequency. Since a Li ion can only hop if a vacancy is nearby, the Li hopping frequency is related to concentration and hopping frequency [ see eqs. (2) and (3) ] of the defects by l/z(Li) = c ( T)( l/z) .
second sample . . . . . o. ( d i f f e r e n t p i e c e s )
(4)
(5)
........ o//. . . . . . o
I
2
I
3
I
I
4 5 IO00/T (K -~)
I
6
/,i
,
,
I
8 10
I
Fig. 2. Spin-lattice relaxation rate of ~Li at 34.99 MHz in two different specimens: ( A ) sample discussed in ref. [2]; (O) piece "B", (@) piece "C" of this work. The various lines are guides to the eye. sible for the pronounced rate maximum at 302 K; at the maximum o~(I)z ~ 1. Part of our 7Li relaxation results is shown in fit'.. 2 together with data from investigations of the ",,~...d'" single crystal [2]. For the new data three temperatufa re~irno,: c.~n be distinguished. Below about 250 K, T~ is extremely large, of the order of 100 s and only weakly dependent on temperature. In the second range, between 250 and 500 K, T~ decreases with rising temperature but is still relatively large. The T~ values in these two regimes depend on the particular "piece" that has been cut out of the single crystal. Finally, around 650 K a rate maximum is reached whose value and corresponding temperature are the same for all pieces. We thus conclude that relaxation in the low and medium tc~nper~ur~, r~g~me~ arises from dipolar interaction of the 7Li m~clei with s~ationary defects and paramagnetic ions whose concentration varies along the crystal. At very low temperatures relaxation could be breught about just by spin diffusion while in the medium temperature regime probably panicle and/or spin diffusion are involved. The analysis of these data is hampered by
4. Evaluation of parameters
The parameters entering eqs. ( 1 ) to (4) can be determined as follows. From a fit of A T 2 to the low temperature 127I relaxation data we get the parameter A. By subtracting A T 2 from 1/T(I) we obtain the second term of eq. (1) which we call for shah l/ T~aifr. The low temperature side of this curve where c(T),~,co and og(I)z>> 1, immediately yields Era. From the maximum of I/T~ d+rrat 306 K, determined by w ( I ) r ( 3 0 6 K ) = I , Zo follows. At very high temperatures where oJ(l)r << 1, we have (6)
l/Tlaiff= Bc( T ) z .
Thus the slope of the relaxation curve yields E r a - E r / 2 and hence El. Knowint, z we can calculate its value for the 7Li rate maximum at 645 K where o~(Li)z(L1) = 1. Then eq. ( 5 ) yields c ( 645 "l~,). x This value *,,-~*~,o-with ,,~,,,,-, I,.t 11 aifr (645 K) determines g. Since we may assume that Co<< c (645 K) we obtain c' from eq. (2). The last parameter, the extrinsic concentration Co, same values at 306 and at 625 K. The deduced numerical values of the parameters are: Co=2.86×10 -6,
c'=98.8,
Ef=l.22eV,
Zo= 1.34X 10-t4 s, Em=0.354 e V , A = l . 4 2 5 X 1 0 - 3 s - t K -2,
B = I . 9 4 6 X 1 0 zTs -2
1092
M. Mali et al.FLi and ~2ZlNMR in Lil single crystals
The solid line in fig. 1 is a fit to the data using these parameters. We notice that both Em and Ef agree quite well with the values 0.39 and 1.12 eV, respectively, obtained from conductivity data [ 3 ]. The extrinsic defect concentration co= 2,86 ppm is remarkably low proving the high quality of sections "B" and "C" of the crystal. The thermally activated number of defects is only about 0.004 ppm at room temperature but increases to about 70 ppm at 500 K. The prefactor % is too low but probably can be explained by entropy effects.
D= ( r2)/6r(Li), where the mean square displacement ( , 2 ) of a Li ion is the only adjustable parameter. Excellent agreemerit with our previous results [ 2 ] for D is obtained if we choose ( r 2) t~2=4.24 A which is the separation of nearest Li sites. This result provides strong support for the validity of the combined analysis of the relaxation data of stationary and mobile ions.
References 5. Calculation of diffusion coefficient Using the parameters just obtained we can predict the Li diffusion coefficient D by means of the Einstein equation
[ 1] C.C. Liang,J. Electrochem. Soc. 120 (1973) 1289. [ 2 ] J.L. Bjorkstam,D. Brinkmann, M. Mali, J. Roos, J.B. Phipps and P.M. Skarstad, Solid State Ionics 18/19 (1986) 557. [ 3 ] J.B. Phipps, Ph.D. Thesis (Department of Material~ Science and Engineering, Northwestern University, 1983).
"lLi AND 1271 NMR IN LiI SINGLE CRYSTALS M. MALl, J. ROOS, D. BRINKMANN Physik-lnstitut, Ur,iversitiit Ziirich, 8001 Zurich, Switzerland
J.B. PHIPP~ and P.M. SKARSTAD Medtronic, Inc., Brooklyn Ctr., MN 55430, USA Received 14 August 1987
We have measured tb ."NMR spin-lattice relaxation times of both the stationary 127I and the mobile VLi nuclei in a new single crystal which has been gi own with extreme care in order to keep any impurity content very low. The high temperature relaxation data can consistently be explained by phonon and vacancy diffusion mechanisms. The relevant parameters thus obtained (vacancy concentration as function of temperature with formation energy 1.22 eV and migration energy 0.35 eV, etc.) have been used to predict a Li diffusion coefficient that is in perfect agreement with our previous measurements.
1. Introduction
2. Experimental details
Since the discovery of Liang [ 1 ] that dispersed phase samples of LiI.AI203 showed substantially increased Li conductivity, interest in such materials has greatly increased. In a previous publication [ 2] we have reported NMR studies which aimed to separate features which are characteristic of the bulk from those related to defect and inteffacial effects. We had presented some preliminary results on dispersed phase LiI.SiO2 and LiI.AI203 but had focused attention upon properties of a "'pure" single crystal. During that work it turned out that the single crystal was not of the quality needed for our investigation. The results were puzzling and not fully understood; there were indications that the single crystal was inhomogeneous. Because an understanding of the LiI single crystal properties is a prerequisite for analyzing the data of ~he dispersed phase systems of Lii we have repeated our studies in a new single crystal specimen and have extended them to the re!axation ~f~he ~ ~.ienar-: :;'i nucieL In this paper we report on the first results of these new studies, in particular we will show how the combination of Li and ! data allows us to determine all the relevant parameters such as the number of mobile ions and various activation energies for the Li diffusion.
The single crystals were prepared from LiI obtained from Anderson Physics Laborato~,, Inc., ~Yrbana, IL. The LiI was used as received without further purification. Transfers of material to NMR tubes were carried out quickly in a vacuum atmosphere glovebox filled with helium. Care was taken to minimize exposure of the Li! ~o the atmosphere of ~he glovebox, which was maintained below 100 ppm H20. The free-flowing spheroidal particles of LiI facilitated the transfers and minimized water contamination by having a favorable ratio of surface to volume. The charged NMR tubes were sealed under 0.5 atm He. Single crystals were then grown directly by the Bridgman technique. The crystals were clear throughout; no regrowth or further purification steps were carried out. Single crystals used in earlier experiments [ 2] were grown Lii w'fich had been prepared by dehydration O~P--,~,---~;~ gr~d~ hydrated ~..~ obtained from Alfa Products, Danvers, MA, as described previousi~ [3 ]. In the case of this material, clear material was selected visually from a preliminary growth pass in a larger quartz tube for growth in the NMR tubes. Boules grown subsequently in the NMR tubes appeared on visual inspection to be mainly clear single
0 167-2738/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Paysics Publishing Division)
1090
M. Malt et el.fiLl and t2rl NMR in Lil single crystals
crystals; however, in each case there were significant amounts of polycrystalline white material swept to the top u,"*"~'",:,,,boule, .., which we presume to be lithium oxide. The N M R experiments were performed with a Bruker SPX pulse spectrometer. The 7Li signals were investigated at 2.11 and 0.47 T corresponding to 34.99 and 7.777 MHz, respectively, while the 127I resonance was detected at 2.11 T (18.02 MHz). The spin-lattice relaxation times T~ were measured by either the ,,t-T-it/2 pulse sequence or the 7t/2-T- it/ 2 saturation method. In either case the magnetization recovery was recorded as the free induction decay. When starting with the 7Li relaxation studies we noticed a tremendous dependence of the magnitude of the low temperature Tt values with respect to the position in the single crystal. Sections could be found where T! is up to 40 times larger than values found in the "old" single crystal investigated previously [ 2 ]. Most important, in these sections the Li magnetization recovers exponentially at nearly all temperatures in contrast to a substantial departure from exponential recovery, in our "old" crystal. Simple exponential recovery, is expected for a homogeneous specimen and 1: the absence of quadrupolar splittings. (The cubic symmetry of the Li site leads to zero splitting.) Thus our results prove the better quality of the new single crystal but also its inhomoge:: city. Hence the new specimen was cut into four pieces denoted by A, B, C, and D with "A" and " D " belonging to the ends and "B" and "C" to the center section of the sinEde crystal. These pieces were investigated separately.
3. Iodine and lithium relaxation data The temperature dependence of the t27][relaxation rate in piece "B" has been plotzed in fig. 1. At temperatures where the magnetization recovery was not exponential we have simply plotted the time at which the magnetization had recovered to e- t times its initial value. TI,. 127I relaxation rate data can be fitted by 1/Tt(I)=AT2+Bc(T)[z/(I+co2(I)z2)].
(l)
Both terms describe relaxation arising from thc in-
1 I
i
!
tzrI
\ ' , j o:,o\
""
.elit) t,,,.,=l
i
/6 i , ,~ --
in L i I single crystol v = 18.022MHz
1
\
i--" 10 z "" ~ ' o ~ 0 . . " ~A'°X~o \ 10
i
2
I
3
i
4 1ooo/1
-
810
[K-']
Fig. !. Spin-lattice relaxation rate of 1271at 18.022 MHz in piece "B" of the new single crystal whose 7Li data are given by O in fig. 2. The solid line is a fit ofeq. (1) to the data, the dashed line is an extrapolation of the term AT 2 of eq. (1) to higher temperatures.
teraction of the 1 2 7 I nuclear electric quadrupole moment eQ with fluctuating electric field gradients (EFG). The first term where T is the temperature, describes relaxation due to acoustical lattice vibrations (Raman process). This mechanism dominates relaxation at low temperatures; the extrapolation of its contribution from low to high temperatures is denoted by the dashed line in fig. 1. The second te:'m in eq. (1) which dominates relaxation at high temperatures, arises from the interaction with fluctuating EFG's set up by diffusing defects such as impurities or vacancies. Their concentration c(T) =Co + c ' e x p ( - E f l 2 k T )
(2)
contains a temperature independent extrinsic part Co and a thermally activated intrinsic contribution where Ef is the formation energy, a~(I)/2~ is the 127I Larmor frequency and r is the correlation time of the fluctuating EFG tensor. We identify as usually 1/ r with the mean hopping frequency of the mobile defects, and assume this frequency to be thermally activated: 1/z = (1/Zo) exp( - E m / k T ) ,
(3)
where Em is the migration energy. The steep rise of the rate above 400 K is caused by the increase of the defect concentration. The term co in c(T) is respon-
M. Marl et aL/ZLi and 'Z"lNMR in Lil single crystals
10'
I
l
!
I
I
":~¢ I
I •
I
7Li in LiI single crystals v=34.990MHz
,~'"~'~" .
,A
1
~...
"
""
"
~- 1C/+
First sample
...
-, 0
-a . . . . .
.zx.//,,,_-a- 4x
.. •
.. Q
,.°
'~
-...
10-a _ "'..
,o-3l 1
the inhomogeneity of the specimens and is not relevant to our present problem. The Li relaxation at high temperatures is due to dipolar interaction with fluctuating magnetic fields caused by diffusing defects. We thus describe these data by l/Tt (Li)=Gz(Li)/[ l +to2(Li)r2(Li)] ,
• i.,..=+.e .e.e+.,, ~,
1091
when, we identify the correlation frequency l/r(Li) as the Li ion hopping frequency. Since a Li ion can only hop if a vacancy is nearby, the Li hopping frequency is related to concentration and hopping frequency [ see eqs. (2) and (3) ] of the defects by l/z(Li) = c ( T)( l/z) .
second sample . . . . . o. ( d i f f e r e n t p i e c e s )
(4)
(5)
........ o//. . . . . . o
I
2
I
3
I
I
4 5 IO00/T (K -~)
I
6
/,i
,
,
I
8 10
I
Fig. 2. Spin-lattice relaxation rate of ~Li at 34.99 MHz in two different specimens: ( A ) sample discussed in ref. [2]; (O) piece "B", (@) piece "C" of this work. The various lines are guides to the eye. sible for the pronounced rate maximum at 302 K; at the maximum o~(I)z ~ 1. Part of our 7Li relaxation results is shown in fit'.. 2 together with data from investigations of the ",,~...d'" single crystal [2]. For the new data three temperatufa re~irno,: c.~n be distinguished. Below about 250 K, T~ is extremely large, of the order of 100 s and only weakly dependent on temperature. In the second range, between 250 and 500 K, T~ decreases with rising temperature but is still relatively large. The T~ values in these two regimes depend on the particular "piece" that has been cut out of the single crystal. Finally, around 650 K a rate maximum is reached whose value and corresponding temperature are the same for all pieces. We thus conclude that relaxation in the low and medium tc~nper~ur~, r~g~me~ arises from dipolar interaction of the 7Li m~clei with s~ationary defects and paramagnetic ions whose concentration varies along the crystal. At very low temperatures relaxation could be breught about just by spin diffusion while in the medium temperature regime probably panicle and/or spin diffusion are involved. The analysis of these data is hampered by
4. Evaluation of parameters
The parameters entering eqs. ( 1 ) to (4) can be determined as follows. From a fit of A T 2 to the low temperature 127I relaxation data we get the parameter A. By subtracting A T 2 from 1/T(I) we obtain the second term of eq. (1) which we call for shah l/ T~aifr. The low temperature side of this curve where c(T),~,co and og(I)z>> 1, immediately yields Era. From the maximum of I/T~ d+rrat 306 K, determined by w ( I ) r ( 3 0 6 K ) = I , Zo follows. At very high temperatures where oJ(l)r << 1, we have (6)
l/Tlaiff= Bc( T ) z .
Thus the slope of the relaxation curve yields E r a - E r / 2 and hence El. Knowint, z we can calculate its value for the 7Li rate maximum at 645 K where o~(Li)z(L1) = 1. Then eq. ( 5 ) yields c ( 645 "l~,). x This value *,,-~*~,o-with ,,~,,,,-, I,.t 11 aifr (645 K) determines g. Since we may assume that Co<< c (645 K) we obtain c' from eq. (2). The last parameter, the extrinsic concentration Co, same values at 306 and at 625 K. The deduced numerical values of the parameters are: Co=2.86×10 -6,
c'=98.8,
Ef=l.22eV,
Zo= 1.34X 10-t4 s, Em=0.354 e V , A = l . 4 2 5 X 1 0 - 3 s - t K -2,
B = I . 9 4 6 X 1 0 zTs -2
1092
M. Mali et al.FLi and ~2ZlNMR in Lil single crystals
The solid line in fig. 1 is a fit to the data using these parameters. We notice that both Em and Ef agree quite well with the values 0.39 and 1.12 eV, respectively, obtained from conductivity data [ 3 ]. The extrinsic defect concentration co= 2,86 ppm is remarkably low proving the high quality of sections "B" and "C" of the crystal. The thermally activated number of defects is only about 0.004 ppm at room temperature but increases to about 70 ppm at 500 K. The prefactor % is too low but probably can be explained by entropy effects.
D= ( r2)/6r(Li), where the mean square displacement ( , 2 ) of a Li ion is the only adjustable parameter. Excellent agreemerit with our previous results [ 2 ] for D is obtained if we choose ( r 2) t~2=4.24 A which is the separation of nearest Li sites. This result provides strong support for the validity of the combined analysis of the relaxation data of stationary and mobile ions.
References 5. Calculation of diffusion coefficient Using the parameters just obtained we can predict the Li diffusion coefficient D by means of the Einstein equation
[ 1] C.C. Liang,J. Electrochem. Soc. 120 (1973) 1289. [ 2 ] J.L. Bjorkstam,D. Brinkmann, M. Mali, J. Roos, J.B. Phipps and P.M. Skarstad, Solid State Ionics 18/19 (1986) 557. [ 3 ] J.B. Phipps, Ph.D. Thesis (Department of Material~ Science and Engineering, Northwestern University, 1983).