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Conductivity enhancement of lithium bromide monohydrate by Al2O3 particles
Solid State Ionics 7 (1982) 119-123 North-Holland Publishing Company
CONDUCTIVITY ENHANCEMENT OF LITHIUM BROMIDE MONOHYDRATE BY AI203 PARTICLES O. NAKAMURA and J.B. GOODENOUGH Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, UK Received 4 February 1982; in final form 19 March 1982
Lithium bromide monohydrate, LiBr • H20, shows an electrical conductivity of 1.4 X 10 -4 mho cm-1 at 100°C and an activation energy of 57 kJ/mol. If A1203 particles are dispersed into this phase, the conductivity is enhanced by nearly one order of magnitude, but the activation energy remains the same. This result is compatible with a depletion-layer mechanism, but not with the formation of a higher hydrate.
<"
1. Introduction Enhancement of the Li+-ion conductivity of LiI by the addition of small particles of alumina [1,2] has aroused considerable experimental and theoretical interest [ 3 - 9 ] . Three 9bservations have emerged from this work: (i) Enhancement of the cationic conductivity of a "stoichiometric"-halide electrolyte by the addition of a dispersed oxide phase is a quite general phenomenon. (ii) For a given concentration of dispersant, the magnitude of the enhancement increases with decreasing particle size and passes through a maximum with increasing concentration of dispersant. (iii) At least three enhancement mechanisms need to be considered: (1) formation of a space-charge layer at the interface [3], (2) formation of a hydrate phase at the interface due to the presence of bound water at the surface of the dispersant particles [4], and (3) creation of bulk lattice-defect dopant centers as a result of thermal-expansion mismatch between dispersant and electrolyte [5]. In this paper we report the enhancement of the conductivity of a halide monohydrate, LiBr • H 2 0 , by the addition of dispersed A1203, and we argue that the observed enhancement of the pre-exponential factor of the conductivity is consistent with a space-charge model.
0 167-2738/82/0000-0000[$ 02.75 © 1982 North-Holland
H~gh-t emp
Phase
Low-temp
Pm 3m a = 4 027 "~
Phase
Pmma a= 7974,
b = 4 054
c : 4015~
Fig. 1. Structure of LiBr • H20. The monohydrate LiBr • H 2 0 has a melting temperature T m = 159°C [10] and crystallizes in the structure shown in fig. 1 [11]. The Br- ions and H 2 0 molecules form a CsCl-type subarray, and the Li + ions occupy octahedral sites coordinated by two axial H 2 0 molecules and four planar B r - ions. The orientation of the water molecules becomes ordered below a transition temperature T t = 34°C [12], and the crystal symmetry is reduced from cubic P m 3 m 01 O-form) to orthorhombic Pmma--DSh (a-form). In the orthorhombic phase the Li + ions order with the H20-molecule orientation so as to minimize the electrostatic repulsive forces between Li + ions and nearest-neighbor protons. The Li + ions occupy, therefore, the octahedral sites perpendicular to the plane
o. Nakamura, ZB. Goodenough /Conductivity enhancement of LiBr. H20
120
of the water molecules, and these sites are just f'dled by one Li+ ion per LiBr • H 2 0 molecule. In this phase, the Li+-ion conduction eLi
= (A/T) exp(-EA/kT )
(1)
has an activation energy that must include both the enthalpy AHg for creation of a mobile ion and the enthalpy A H m for migration of the ion: EA(T
< Tt) ..~ A H m + 1AHg.
(2)
Although disordering of the H20-molecule orientations in the cubic phase makes all the 2H20 4Broctahedral sites appear crystallographically equivalent to X-ray diffraction, the Li+-ion distribution must in fact be correlated with the local H20-molecule orientations so as to optimize the electrostatic Madelung energy. Nevertheless, disorder creates a significant, essentially temperature-independent concentration of mobile ions, so the creation enthalpy M/g drops out of the activation energy: E A ( T > Tt) "~ AH m .
(3)
Archer and Armstrong [13] have reported a definite change in E A at T t for the conductivity of LiBr • H20; the ctiange is characteristic of a smooth orderdisorder transition of the type described with EA(T < Tt) > EA(T > Tt). An enhancement at T > T t of the conductivity of LiBr • H 2 0 by the introduction of dispersed A1203 particles can provide an important distinction between the three enhancement mechanisms that have been proposed provided the temperature dependence of the Li÷-ion conductivity of a higher-hydrate phase is known. In a companion paper, we give the temperature dependence of the conductivity of a mixed LiBr • 2H20 + LiBr • H 2 0 sample [14] ; it is totally different from the resuits reported in this paper for LiBr • H 2 0 with/ without A1203 particles.
H 2 0 was obtained by drying the aqueous LiBr solution in the same way. All the composites were identified by X-ray powder diffraction. The sample powder was sandwiched between flakegraphite electrodes and pressed into a pellet in a 7 mm diameter steel die under a pressure of 2000 kg/ cm 2 ; ac conductance was measured by inspection of the complex admittance plot obtained with a Hewlett-Packard 4800 A vector impedance meter. Since the samples were hygroscopic, all mounting operations were made in an M-filled glove-box. Also, the conductivity measurements were done with a home.made conventional cell under an atmosphere of dry argon.
3. Results and discussion
The temperature dependence of the electrical conductivity of LiBr • H 2 0 with/without the addition of dispersed, 0.05/am 3,-A1203 particles is well described by the phenomenological equation (1), see fig. 2. Absorbed water on our sample produced a parallel surt/*£ 150
]00
10-2
50
i
20
i
10-3 57 k J / rnol 7
E
o E
10-6]
O LiBr
3/oc
H20
L i B r H20 : AI203 (] :1) [] LiBr
H20 : A I 2 0 3 ( 2 : 1 )
2. Experimental ~0-7[ The LiBr and Al203 were of commercial origin. BDH polishing grade ¢t-A1203, particle size 1.0/am and 0.3/am, and 0.05 pan ~/-A1203 were used. The composites of LiBr • H 2 0 and A1203 were obtained by drying overnight the aqueous LiBr solution with dispersed A1203 particles in a 120°C oven. LiBr •
21s
3~.o
3'.s
kKIT
Fig. 2. Temperature dependence of the electrical conductivity of the IABr • H20-A1203 system: o: LiBr • H20, ~: LiBr • H20-A1203 (1 : 1), and m: LiBr- H20-AI~O a (2 : 1). The particle size of A1203 is 0.05 tzm.
O. Nakamura, J.B. Goodenough / Conductivity enhancement of LiBr. H20 face conductance that prevented us from measuring lower conductivities with any accuracy; consequently we Were unable to verify the discontinuity in E A at T t reported by Archer and Armstrong [13]. As our curve for LiBr. H 2 0 without A1203 addition is similar t0 theirs, we have no reason to doubt their £mding. ' The activation energy E A = 57 kJ/mol found for all our samples is similar to the E A = 63 kJ/mol reported [4] for isostructural LiI • H20. It is therefore surprising that the conductivity at 100°C of LiBr • H20, 1:4 X 10 - 4 mho cm -1 , is an order of magnitude lower than that of the iodine analogue at this temperature (1.1 X 10 - 3 mho cm -1 [9]). This result implies that LiI • H 2 0 has the larger pre-exponential factor A ~ c(1 - c)exp(AS m + ½ASg),
121
E o E -4"
o
5
°
L~Br H20
oo o
AI203 (0,05p) ( 0 0
--
5~0
~00
u
2 E
(4)
and hence the larger concentration c and/or entropy (AS m + ½ASg) of mobile Li+ ions at T > T t. Moreover the fact that E A is insensitive to A1203 addition indicates that the pronounced conductivity enhancement changes A, but not the charge-carrier conduc. tion mechanism responsible for eq. (3). The dependence of the conductivity at 100°C on concentration of 0.05/lm 7-A1203 particles and on AI203 particle size are shown in fig. 3. They are qualitatively similar to analogous plots of A1203-enhanced LiI conductivity [2]. The characteristic features are an evident indication that the enhancement increases with the area of the interface between particle and electrolyte; the optimum particle concentration provides a measure of the thickness of the electrolyte layer at the interface where enhanced conductivity occurs.
The fact that E A remains constant with AI203particle addition enables us to eliminate higherhydrate formation as the enhancement mechanism. Were higher-hydrate formation responsible, the temperature dependence of the conductivity should reflect that of a LiBr .H20 , LiBr • 2H20 mixture; but we have shown [14] that such a mixture has a completely different temperature dependence of the conductivity. Two other enhancement mechanisms remain to be considered: formation of a space-charge layer and formation of strain-induced Li+-ion acceptors. Since eq. (3) appears to hold in the temperature range in-
o2
0 0105
L
i
0.3
~,0
AI203
particle size ! ,u
Fig. 3. Conductivity o f LiBr • H 2 0 - A I ~ O a system as a function o f (a) A1203 (0.05 um) content and (b) AI203 particle size (LiBr • H 2 0 - A I 2 0 a 2 : 1).
vestigated (T > Tt = 34°C), either mechanism must enhance only the pre-exponential factor A of eq. (4) within a fairly thin layer of electrolyte at the particle/ electrolyte interface. This constraint means that any Li+-ion acceptors introduced by thermal mismatch must not capture the Li+-ion vacancies they produce within the enhanced-conductivity layer. Neutral defects should have relatively little influence on the conductivity; point defects that are charged should tend to trap any Li+.ion vacancies they create unless the density of defects greatly exceeds the percolation limit for conduction via a path always near-neighbor to a defect. Any trap energy would add to &Arm, thus increasing E A. In the absence of any obvious model for a strain-induced Li+-ion acceptor that would leave E A unchanged, we ask whether the concept of a space-charge layer can suffice. An oxide particle in an aqueous medium is characterized by a full anion coordination of the surface metal atoms by anions from the water; this is the origin of the bound water at the particle surface. The
122
o. Nakamura, £B. Goodenough /Conductivity enhancement of LiBr. HzO
protons of the bound water distribute themselves over the oxygen surface of the particle; however, the total surface density of bound protons depends on the acidity of the oxide and the pH of the solution. Most of this bound water would be readily accomodated within a particle/LiBr • H 2 0 interface, but some exchange of surface protons for electrolyte Li + ions can be expected to create H30+ and V~i pairs in the electrolyte, where V~i is a Li+-ion vacancy. More irnporta~nt, the greater affinity of Li+ ions for an 0 2 - ion coordination will drive Li+ ions into the particle surface to give the particle a nett positive charge. The Li+-ion vacancies left behind in the electrolyte produce a negative space charge that extends out from the interface. In analogy with an electronic Schottky barrier, the magnitude of the charge transfer depends upon the energy difference AS of the Li+-ion electrochemical potentials in the particle and the electrolyte; the width of the space-charge layer is (ee0 A~b/ 2rrnDe2)l/2, where ee 0 is the dielectric constant of the electrolyte and n D is the density of immobile Li+ion donor sites. Were the Li+-ion donor sites mobile, as at a metal-electrode/liquid-electrolyte interface, the aoalogy would be to a narrow Helmholtz layer. In LiBr. H20, we may expect some Br- ions to occupy H 2 0 positions, corresponding to LiBr.(1-8)H20; these substitutional Br- ions would act as immobile donor centers of the type required for formation of a Schottky.barrier analogue. The Li+.ion vacancies so generated are trapped only in the sense that they are confined to the space-charge layer; within this layer they move with an activation energy E A = AH m that is determined only by the charge-carrier mobility. However, the pre-exponential factor A of eq. (4) may be strongly enhanced provided the concentration c of mobile charge carriers is initially small and/or the entropy factor exp [(ASm + ½ASg)/k] is sensitive to the concentration c of mobile species. To examine this last question, we must consider the conduction mechanism of LiBr. H 2 0 itself. From fig. 1, the perfectly ordered orthorhombic phase would not be a Li+-ion conductor. Occupation of the 2 H 2 0 - 4Br- octahedral sites by Li+ ions is dictated by Li+-H2 O electrostatic forces, and a dynamic distribution over all the possible sites depends upon a dynamic rotation of water molecules. Even in the "disordered state" at temperatures T > T t, Li+-ion mobilities depend upon water-molecule rotations,
and these rotations appear to have a threshold energy near 60 kJ/mol. With a distribution of activation energies for water-molecule rotation, the concentration c o f " m o b i l e " Li + ions at any instant may be small. Moreover, if the entropy for Li+-ion motion increases with the concentration c of mobile vacancies, then the pre-exponential factor of eq. (4) becomes A "~ c(1 - c)exp [(ASmo + ½ASgo + cAS)/k] and increases exponentially with increasing concentration c. Since the entropy term is sensitive to the number of low-energy orientations of the water molecules for a given Li+-ion distribution, an increase in entropy with c may be anticipated. In conclusion, the data reported in this paper are consistent with a space-charge model for the enhancement of the conductivity of LiBr. H 2 0 by dispersed A1203 particles; they do not support a model of higher.hydrate formation. Moreover, we point out that an increase in the entropy of the water molecules with increasing concentration of Li+-ion vacancies introduces into the pre-exponential factor an exponential dependence on this concentration. Similarly, we might expect an exponential dependence on the concentration of unionized donor centers, which could account for the marked differences in preexponential factors reported for LiI • H 2 0 and LiBr • H20. This research was supported by a grant from the European Community Research and Development "Programme and the Air Force Office of Strategic Research. References [1 ] C.R. Schlaikjer and C.C. Liang, J. Electrochem. Soc. 118 (1971) 1447. [2] C.C. Liang, J. Electrochem. Soc. 120 (1973) 1289. [3] T. Jow and J.B. Wagner, Jr., J. Electrochem. Soc. 126 (1979) 163. [4] A.M. Stoneham, E. Wade and J.A. Kilner, Mater. Res. Bull 14 (1979) 661. [5] K. Shahi and J.B. WagnerJr., Solid State Ionies 3/4 (198t) 295. [6] B.B. Owens and H.J. Hanson, US Patent 4007122 (1977). [7] S. Pack, B. Owens and J.B. Wagner, Jr., J. Eleetrochem. Soc. 127 (1980) 1177. [8] P.M. Skarstad, D.R. Merritt and B.B. Owens, Solid State Ionics 3[4 (1981) 277.
O. Nakamura, J.B. Goodenough / Conductivity enhancement of LiBr. 1120 [9] F.W. Poulsen, Solid State Ionics 2 (1981) 53. [10] J.-J. Kessis, Bull. Soe. China. (France) 32 (1965) 48. [11] E. Weiss, H. Hensel and H. Kiihr, Chem. Bet. 102 (1969) 632. [12] P.R. Clayton, A.G. Dunn, S. Holt and L.A.K. Staveley, J. Chem. Soc. Faraday I, 76 (1980) 2362.
123
[13] W.I. Archer and R.D. Armstrong, Electrochim. Acta 26 (1981) 1083. [14] O. Nakamura and J.B. Goodenough, Solid State Ionics 7 (1982) 125.
CONDUCTIVITY ENHANCEMENT OF LITHIUM BROMIDE MONOHYDRATE BY AI203 PARTICLES O. NAKAMURA and J.B. GOODENOUGH Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, UK Received 4 February 1982; in final form 19 March 1982
Lithium bromide monohydrate, LiBr • H20, shows an electrical conductivity of 1.4 X 10 -4 mho cm-1 at 100°C and an activation energy of 57 kJ/mol. If A1203 particles are dispersed into this phase, the conductivity is enhanced by nearly one order of magnitude, but the activation energy remains the same. This result is compatible with a depletion-layer mechanism, but not with the formation of a higher hydrate.
<"
1. Introduction Enhancement of the Li+-ion conductivity of LiI by the addition of small particles of alumina [1,2] has aroused considerable experimental and theoretical interest [ 3 - 9 ] . Three 9bservations have emerged from this work: (i) Enhancement of the cationic conductivity of a "stoichiometric"-halide electrolyte by the addition of a dispersed oxide phase is a quite general phenomenon. (ii) For a given concentration of dispersant, the magnitude of the enhancement increases with decreasing particle size and passes through a maximum with increasing concentration of dispersant. (iii) At least three enhancement mechanisms need to be considered: (1) formation of a space-charge layer at the interface [3], (2) formation of a hydrate phase at the interface due to the presence of bound water at the surface of the dispersant particles [4], and (3) creation of bulk lattice-defect dopant centers as a result of thermal-expansion mismatch between dispersant and electrolyte [5]. In this paper we report the enhancement of the conductivity of a halide monohydrate, LiBr • H 2 0 , by the addition of dispersed A1203, and we argue that the observed enhancement of the pre-exponential factor of the conductivity is consistent with a space-charge model.
0 167-2738/82/0000-0000[$ 02.75 © 1982 North-Holland
H~gh-t emp
Phase
Low-temp
Pm 3m a = 4 027 "~
Phase
Pmma a= 7974,
b = 4 054
c : 4015~
Fig. 1. Structure of LiBr • H20. The monohydrate LiBr • H 2 0 has a melting temperature T m = 159°C [10] and crystallizes in the structure shown in fig. 1 [11]. The Br- ions and H 2 0 molecules form a CsCl-type subarray, and the Li + ions occupy octahedral sites coordinated by two axial H 2 0 molecules and four planar B r - ions. The orientation of the water molecules becomes ordered below a transition temperature T t = 34°C [12], and the crystal symmetry is reduced from cubic P m 3 m 01 O-form) to orthorhombic Pmma--DSh (a-form). In the orthorhombic phase the Li + ions order with the H20-molecule orientation so as to minimize the electrostatic repulsive forces between Li + ions and nearest-neighbor protons. The Li + ions occupy, therefore, the octahedral sites perpendicular to the plane
o. Nakamura, ZB. Goodenough /Conductivity enhancement of LiBr. H20
120
of the water molecules, and these sites are just f'dled by one Li+ ion per LiBr • H 2 0 molecule. In this phase, the Li+-ion conduction eLi
= (A/T) exp(-EA/kT )
(1)
has an activation energy that must include both the enthalpy AHg for creation of a mobile ion and the enthalpy A H m for migration of the ion: EA(T
< Tt) ..~ A H m + 1AHg.
(2)
Although disordering of the H20-molecule orientations in the cubic phase makes all the 2H20 4Broctahedral sites appear crystallographically equivalent to X-ray diffraction, the Li+-ion distribution must in fact be correlated with the local H20-molecule orientations so as to optimize the electrostatic Madelung energy. Nevertheless, disorder creates a significant, essentially temperature-independent concentration of mobile ions, so the creation enthalpy M/g drops out of the activation energy: E A ( T > Tt) "~ AH m .
(3)
Archer and Armstrong [13] have reported a definite change in E A at T t for the conductivity of LiBr • H20; the ctiange is characteristic of a smooth orderdisorder transition of the type described with EA(T < Tt) > EA(T > Tt). An enhancement at T > T t of the conductivity of LiBr • H 2 0 by the introduction of dispersed A1203 particles can provide an important distinction between the three enhancement mechanisms that have been proposed provided the temperature dependence of the Li÷-ion conductivity of a higher-hydrate phase is known. In a companion paper, we give the temperature dependence of the conductivity of a mixed LiBr • 2H20 + LiBr • H 2 0 sample [14] ; it is totally different from the resuits reported in this paper for LiBr • H 2 0 with/ without A1203 particles.
H 2 0 was obtained by drying the aqueous LiBr solution in the same way. All the composites were identified by X-ray powder diffraction. The sample powder was sandwiched between flakegraphite electrodes and pressed into a pellet in a 7 mm diameter steel die under a pressure of 2000 kg/ cm 2 ; ac conductance was measured by inspection of the complex admittance plot obtained with a Hewlett-Packard 4800 A vector impedance meter. Since the samples were hygroscopic, all mounting operations were made in an M-filled glove-box. Also, the conductivity measurements were done with a home.made conventional cell under an atmosphere of dry argon.
3. Results and discussion
The temperature dependence of the electrical conductivity of LiBr • H 2 0 with/without the addition of dispersed, 0.05/am 3,-A1203 particles is well described by the phenomenological equation (1), see fig. 2. Absorbed water on our sample produced a parallel surt/*£ 150
]00
10-2
50
i
20
i
10-3 57 k J / rnol 7
E
o E
10-6]
O LiBr
3/oc
H20
L i B r H20 : AI203 (] :1) [] LiBr
H20 : A I 2 0 3 ( 2 : 1 )
2. Experimental ~0-7[ The LiBr and Al203 were of commercial origin. BDH polishing grade ¢t-A1203, particle size 1.0/am and 0.3/am, and 0.05 pan ~/-A1203 were used. The composites of LiBr • H 2 0 and A1203 were obtained by drying overnight the aqueous LiBr solution with dispersed A1203 particles in a 120°C oven. LiBr •
21s
3~.o
3'.s
kKIT
Fig. 2. Temperature dependence of the electrical conductivity of the IABr • H20-A1203 system: o: LiBr • H20, ~: LiBr • H20-A1203 (1 : 1), and m: LiBr- H20-AI~O a (2 : 1). The particle size of A1203 is 0.05 tzm.
O. Nakamura, J.B. Goodenough / Conductivity enhancement of LiBr. H20 face conductance that prevented us from measuring lower conductivities with any accuracy; consequently we Were unable to verify the discontinuity in E A at T t reported by Archer and Armstrong [13]. As our curve for LiBr. H 2 0 without A1203 addition is similar t0 theirs, we have no reason to doubt their £mding. ' The activation energy E A = 57 kJ/mol found for all our samples is similar to the E A = 63 kJ/mol reported [4] for isostructural LiI • H20. It is therefore surprising that the conductivity at 100°C of LiBr • H20, 1:4 X 10 - 4 mho cm -1 , is an order of magnitude lower than that of the iodine analogue at this temperature (1.1 X 10 - 3 mho cm -1 [9]). This result implies that LiI • H 2 0 has the larger pre-exponential factor A ~ c(1 - c)exp(AS m + ½ASg),
121
E o E -4"
o
5
°
L~Br H20
oo o
AI203 (0,05p) ( 0 0
--
5~0
~00
u
2 E
(4)
and hence the larger concentration c and/or entropy (AS m + ½ASg) of mobile Li+ ions at T > T t. Moreover the fact that E A is insensitive to A1203 addition indicates that the pronounced conductivity enhancement changes A, but not the charge-carrier conduc. tion mechanism responsible for eq. (3). The dependence of the conductivity at 100°C on concentration of 0.05/lm 7-A1203 particles and on AI203 particle size are shown in fig. 3. They are qualitatively similar to analogous plots of A1203-enhanced LiI conductivity [2]. The characteristic features are an evident indication that the enhancement increases with the area of the interface between particle and electrolyte; the optimum particle concentration provides a measure of the thickness of the electrolyte layer at the interface where enhanced conductivity occurs.
The fact that E A remains constant with AI203particle addition enables us to eliminate higherhydrate formation as the enhancement mechanism. Were higher-hydrate formation responsible, the temperature dependence of the conductivity should reflect that of a LiBr .H20 , LiBr • 2H20 mixture; but we have shown [14] that such a mixture has a completely different temperature dependence of the conductivity. Two other enhancement mechanisms remain to be considered: formation of a space-charge layer and formation of strain-induced Li+-ion acceptors. Since eq. (3) appears to hold in the temperature range in-
o2
0 0105
L
i
0.3
~,0
AI203
particle size ! ,u
Fig. 3. Conductivity o f LiBr • H 2 0 - A I ~ O a system as a function o f (a) A1203 (0.05 um) content and (b) AI203 particle size (LiBr • H 2 0 - A I 2 0 a 2 : 1).
vestigated (T > Tt = 34°C), either mechanism must enhance only the pre-exponential factor A of eq. (4) within a fairly thin layer of electrolyte at the particle/ electrolyte interface. This constraint means that any Li+-ion acceptors introduced by thermal mismatch must not capture the Li+-ion vacancies they produce within the enhanced-conductivity layer. Neutral defects should have relatively little influence on the conductivity; point defects that are charged should tend to trap any Li+.ion vacancies they create unless the density of defects greatly exceeds the percolation limit for conduction via a path always near-neighbor to a defect. Any trap energy would add to &Arm, thus increasing E A. In the absence of any obvious model for a strain-induced Li+-ion acceptor that would leave E A unchanged, we ask whether the concept of a space-charge layer can suffice. An oxide particle in an aqueous medium is characterized by a full anion coordination of the surface metal atoms by anions from the water; this is the origin of the bound water at the particle surface. The
122
o. Nakamura, £B. Goodenough /Conductivity enhancement of LiBr. HzO
protons of the bound water distribute themselves over the oxygen surface of the particle; however, the total surface density of bound protons depends on the acidity of the oxide and the pH of the solution. Most of this bound water would be readily accomodated within a particle/LiBr • H 2 0 interface, but some exchange of surface protons for electrolyte Li + ions can be expected to create H30+ and V~i pairs in the electrolyte, where V~i is a Li+-ion vacancy. More irnporta~nt, the greater affinity of Li+ ions for an 0 2 - ion coordination will drive Li+ ions into the particle surface to give the particle a nett positive charge. The Li+-ion vacancies left behind in the electrolyte produce a negative space charge that extends out from the interface. In analogy with an electronic Schottky barrier, the magnitude of the charge transfer depends upon the energy difference AS of the Li+-ion electrochemical potentials in the particle and the electrolyte; the width of the space-charge layer is (ee0 A~b/ 2rrnDe2)l/2, where ee 0 is the dielectric constant of the electrolyte and n D is the density of immobile Li+ion donor sites. Were the Li+-ion donor sites mobile, as at a metal-electrode/liquid-electrolyte interface, the aoalogy would be to a narrow Helmholtz layer. In LiBr. H20, we may expect some Br- ions to occupy H 2 0 positions, corresponding to LiBr.(1-8)H20; these substitutional Br- ions would act as immobile donor centers of the type required for formation of a Schottky.barrier analogue. The Li+.ion vacancies so generated are trapped only in the sense that they are confined to the space-charge layer; within this layer they move with an activation energy E A = AH m that is determined only by the charge-carrier mobility. However, the pre-exponential factor A of eq. (4) may be strongly enhanced provided the concentration c of mobile charge carriers is initially small and/or the entropy factor exp [(ASm + ½ASg)/k] is sensitive to the concentration c of mobile species. To examine this last question, we must consider the conduction mechanism of LiBr. H 2 0 itself. From fig. 1, the perfectly ordered orthorhombic phase would not be a Li+-ion conductor. Occupation of the 2 H 2 0 - 4Br- octahedral sites by Li+ ions is dictated by Li+-H2 O electrostatic forces, and a dynamic distribution over all the possible sites depends upon a dynamic rotation of water molecules. Even in the "disordered state" at temperatures T > T t, Li+-ion mobilities depend upon water-molecule rotations,
and these rotations appear to have a threshold energy near 60 kJ/mol. With a distribution of activation energies for water-molecule rotation, the concentration c o f " m o b i l e " Li + ions at any instant may be small. Moreover, if the entropy for Li+-ion motion increases with the concentration c of mobile vacancies, then the pre-exponential factor of eq. (4) becomes A "~ c(1 - c)exp [(ASmo + ½ASgo + cAS)/k] and increases exponentially with increasing concentration c. Since the entropy term is sensitive to the number of low-energy orientations of the water molecules for a given Li+-ion distribution, an increase in entropy with c may be anticipated. In conclusion, the data reported in this paper are consistent with a space-charge model for the enhancement of the conductivity of LiBr. H 2 0 by dispersed A1203 particles; they do not support a model of higher.hydrate formation. Moreover, we point out that an increase in the entropy of the water molecules with increasing concentration of Li+-ion vacancies introduces into the pre-exponential factor an exponential dependence on this concentration. Similarly, we might expect an exponential dependence on the concentration of unionized donor centers, which could account for the marked differences in preexponential factors reported for LiI • H 2 0 and LiBr • H20. This research was supported by a grant from the European Community Research and Development "Programme and the Air Force Office of Strategic Research. References [1 ] C.R. Schlaikjer and C.C. Liang, J. Electrochem. Soc. 118 (1971) 1447. [2] C.C. Liang, J. Electrochem. Soc. 120 (1973) 1289. [3] T. Jow and J.B. Wagner, Jr., J. Electrochem. Soc. 126 (1979) 163. [4] A.M. Stoneham, E. Wade and J.A. Kilner, Mater. Res. Bull 14 (1979) 661. [5] K. Shahi and J.B. WagnerJr., Solid State Ionies 3/4 (198t) 295. [6] B.B. Owens and H.J. Hanson, US Patent 4007122 (1977). [7] S. Pack, B. Owens and J.B. Wagner, Jr., J. Eleetrochem. Soc. 127 (1980) 1177. [8] P.M. Skarstad, D.R. Merritt and B.B. Owens, Solid State Ionics 3[4 (1981) 277.
O. Nakamura, J.B. Goodenough / Conductivity enhancement of LiBr. 1120 [9] F.W. Poulsen, Solid State Ionics 2 (1981) 53. [10] J.-J. Kessis, Bull. Soe. China. (France) 32 (1965) 48. [11] E. Weiss, H. Hensel and H. Kiihr, Chem. Bet. 102 (1969) 632. [12] P.R. Clayton, A.G. Dunn, S. Holt and L.A.K. Staveley, J. Chem. Soc. Faraday I, 76 (1980) 2362.
123
[13] W.I. Archer and R.D. Armstrong, Electrochim. Acta 26 (1981) 1083. [14] O. Nakamura and J.B. Goodenough, Solid State Ionics 7 (1982) 125.