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L 12 I i li i 1 M d l fLecture 12 - Ionics applications 1: Models of Ionic Conduction in Chalcogenide Glasses
Steve W. MartinDepartment of Materials Science & Engineeringp & g gIowa State University of Science & TechnologyAmes, IA 50011
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Ion Conduction in GlassI ti ( d ti ) i t i ll li it d i id l
100101 16
0014
0012
0010
0080
060
0
400
200
0Temperature (oC)
Glassy
Ion motion (conduction) is typically very limited in oxide glasses
10-410-310-210-110
Lithium battery operationTg
35Li2 O-30Li
2 SO4 -10(1
10-810-710-610-510 4 10(LiCl)
2 -12.5SiO2 -12.5B
2 O3
25Li2 O-25Al
2 O25L
dc (
-cm
)-
10-1210-1110-1010-910 2 O
3 -50SiO2
5Li2 O -75B
2 O3
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.010-1510-1410-1310
[email protected] Lecture 12: Models of Ionic Conduction in Glass 2
1000 / T (K-1)
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Fast Ion Conduction in Glass
0
101 1600
1400
1200
1000
800
600
400
200
0Temperature (oC)
GlassyCrystallineTgTm-AgIFIC glasses can be
10-1
100 TgTmg
RbAg4I529.8Ag
2O-40.4(AgI
-NaAl11O1735LZ)-1
gmore than 1 million times more conductive!
10-3
10-2
4(AgI)2-29.8P
2O5
28.6Ag2O-42.8(AgI)
2-28.6MoO3
50Ag2 S-5GeS-45G
5Li2 O-30Li
2 SO4 -10(LiCl)
Li4 B
7 O12 Cl26.9L
25Li2 O-25A
ZrO2 -9%
Y2 O
3
dc (
-cm
5
10-4
0 GeS2
Cl)2 -12.5SiO
2 -12.5B2 O
3
9Li2 O-9(LiCl)
2 -64.1B2 O
LiAlSiO4
5Al2 O
3 -50SiO2
25Li2 O -75B
2 O
LiNbO3
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 010-6
10-5
3
O3
42 O3
3
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.01000 / T (K-1)
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Li-ion Battery: The Most Common Li battery
C6 is a common anode t i l f Li i b tt i
e-
material for Li-ion batteries
The maximum capacity of graphite (LiC ): ~350Ah/kg
Li+e-
e-
graphite (LiC6): ~350Ah/kg
Li: ~ 4000 Ah/kgLi+
Li+e-
e-
e-
-
Li C6 Li CoOLi+ conducting C6 has good cycle-life,
e e-
LixC6 Li1-xCoO2co duct g
electrolyteAnode: LixC6 xLi+ + xe- + C6
Cathode: Li CoO + xLi+ + xe- LiCoO
But low capacity for new portable devices
Cathode: Li1-xCoO2 + xLi+ + xe LiCoO2
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Anode and Cathode Combinations Determine the Energy Density of Lithium Batteries
Cathodes
Density of Lithium Batteries
Anodes
J.M. Tarascon, M. Armand, Nature, 414, 15 (2001) 359
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Lithium Dendrite Formation in Li ion Batteries
Li metal
Non-epitaxial deposition of lithium after each cycle leads to the growth of uneven “fingers” or dendrites of lithiumuneven fingers or dendrites of lithium
Internal dendrites result in short circuits of the battery – heat and fire
M. Dolle et al. Electrochemical and Solid-State Letters, 5(12) (2002)A286
Lecture 12: Models of Ionic Conduction in Glass
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Fast Ion Conduction in Glass
Can highly conducting glasses be used in Lithium g y g gbatteries To increase safety?
By mitigating lithium dendrite formation
To increase energy density? By enabling lithium metal (or similar high activity) anodes By enabling lithium metal (or similar high activity) anodes
To reduce cost? By simplifying design and using lower cost materials
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Fast Ion (Li+) Conducting Sulfide Glasses-Ioni Ch l ogenide Gl ssesIonic Chalcogenide GlassesCharge Compensated Chalcogenide Glasses
Typical glass compositions Lithium salt + + glass former + additives
Lithium modifierLithium modifier
Mobile cations Glass structure Chemical/mechanical/Mobile cations Glass structure Chemical/mechanical/electrochemical durability
LiI + Li2S + SiS2 B2S3 GeS2 LiI + Li2S + SiS2, B2S3, GeS2 … LiI + Li2S + GeS2+ Ga2S3, La2S3, ZrS2…
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Example: Structures of xLi2S +(1-x)GeS2 Glasses
385
340s (Ge-S-)s (Ge-S-Ge)
Raman
xLi2S + (1-x)GeS2
415374 (Ge-S-Ge)
(Ge-S-)IR
454
415340
0.5
0.55
x = 0.6
tens
ity (a
.u.)
446
0.55
x = 0.6
sorb
ance
(a.u
.)
0.0
0.3
0.40.45In
t
200 300 400 500 600 700
0.00.30.4
0.450.5A
bs
200 300 400 500 600 700Wavenumber (cm-1)
200 300 400 500 600 700
Wavenumber (cm-1)
Ge S
S
S
Ge S
S
S
S
Li+
Li+Ge
S-
S Ge SS
S-
S- S-
Li+ Li+
Ge
S-
S S-
S-
Li+
Li+
Li+Ge S
S-
S-
Li+
Li+
-SLi+
GeS4/2 (GeS3/2S)-
S SLi+ Li+
(GeS2/2S2)2-
Li Li
(GeS1/2S2)3-
Lecture 12: Models of Ionic Conduction in Glass
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Arrhenius Ionic Conductivity
100
101 1600
1400
1200
1000
800
600
400
200
0Temperature (oC)
GlassyCrystallineTgTm-AgI
10-1
10RbAg4I5
29.8Ag2O-40.4(AgI)
2-29 8P
-NaAl11O17
2
35Li2 O
ZrOm)-1
10-3
10-22 29.8P
2O5
28.6Ag2O-42.8(AgI)
2-28.6MoO3
50Ag2 S-5GeS-45GeS
2
2 O-30Li2 SO
4 -10(LiCl)2 -12 5
Li4 B
7 O12 Cl26.9Li
2 O-9
25Li2 O-25Al
2 O
O2 -9%
Y2 O
3
dc (
-cm
10-5
10-4
22.5SiO2 -12.5B
2 O3
-9(LiCl)2 -64.1B
2 O3
LiAlSiO4
2 O3 -50SiO
2
25Li2 O -75B
2 O3
LiNbO3
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.010-6
1000 / T (K-1)000 / ( )
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Raman Spectra of NaI doped glasses
1-NBS451
yNaI+(1-y)[0.3Na2S+0.7(0.1Ga2S3+0.9GeS2)]
U ll lk li451
y=0.1
y=0.2
a.u.
)
Usually, alkali iodide (MI) resides in the
3740-NBS
331
y=0
0 2nten
sity
(a interstitials of glass structure network and
3-NBS390
y=0.1
y=0.2
y=0
yNaI+(1 y)[0 6Na S+0 4(0 1Ga S +0 9GeS )]
In network and causes no change in the glass
t k t t150 200 250 300 350 400 450 500 550
yNaI+(1-y)[0.6Na2S+0.4(0.1Ga2S3+0.9GeS2)]
Wavenumber (cm-1)
network structure
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Relation of glass structure to ionic conduction
xNa2O + (1-x)SiO2Glass in 2-D
+ +
+
|E|+ +
++ +
BO
++
ergy
- +
NBO NBO
BO
-++1/rn
Es = Strain EnergyEc = Coulomb Energy
Ene Eact s Ec
r r
EC
ES
-e2/r
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Ionic Conduction in Glass
= neZ N is the number density
eZ is the charge +1 most of
Calculation: Take:
22 3 eZ is the charge, +1 most of the time
is the mobility
n ~ 1022 M+/cm3
A-M Universities… ~ 10-9 (cm)-1 Oxide glass
Estimation: What are the units of n? What is the approximate
What is ? N-Z Universities… ~ 10-3 (cm)-1 Sulfide glassat s t e app o ate
magnitude of n for a glass? What are the units of eZ? What is it magnitude for Li+?
10 (cm) Sulfide glass What is ?
Compare Si What is it magnitude for Li ? What are the units of ?
What is the conductivity of a typical n doped Si?
What is ?
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DC ion conductivity in glass
Arrhenius temperature dependence
xLi2O + (1-x)P2O5
Creation of non-bridging oxygens
“Mobile” lithium ions The higher the
concentration of Li2O, 2 ,the higher the conductivity Lower resistivity
Activation energy decreases with Li2Ocontent
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S. Martin, C.A. Angell JNCS ’83
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Chalcogenide Glasses have significantly higher conductivities
Salt doped lithium phosphate and thiophosphate glasses dc act
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Relation of Glass Structure to Ionic Conduction
xNa2O + (1-x)SiO2Glass in 2-D
+ +
+
|E|+ +
++ +
BO
++
ergy
- +
NBO NBO
BO
-++1/rn
Es = Strain EnergyEc = Coulomb Energy
Ene Eact s Ec
r r
EC
ES
-e2/r
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Mobility and Number Dependence of the Conductivity
RT
ET
TeZTnT actc exp)()()( 0
RT
EnTn c
o exp)( RT
ET sexp)( 0
RTT
T exp)(
EEenZ
Question: What are the magnitudes of E and E ?
RT
EET
enZT scc exp)( 00
Question: What are the magnitudes of ES(M) and EC ?
Lecture 12: Models of Ionic Conduction in Glass
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Short Range Order Models
Anderson-Stuart Model Assignment of Coulombic and Strain energy terms, EC + Es
“Creation” or Concentration versus Migration energy terms, EC + Es
Coulomb energy term, EC attractive force between cation and anion
2)(
1)(2/
2.
22.
ac
acstruct
ac
acacstruct
rreZZC
rreZZeZZC
For Li+ in a oxide and sulfide glass Homework, Take Cstruct / ~ 1
What are the approximate values of rc, rd, and ? What is the approximate magnitude of EC?
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Short Range Order Models
Strain energy term - Es
“Work” required to “dilate” the network so large cations i tcan migrate
E G r rS c d ( ) /2 2
G Sh d l
Cation size affect on Strain Energy
40
50
G Shear modulusrc Cation radiusrd Interstitial site radius
10
20
30
40
E s
(kca
l/mol
e)
Jump distance0
10
0 0.04 0.08 0.12 0.16 0.2
Cation Radius (nm)
For Li+ in an oxide and sulfide glass Homework What are the approximate values of rc, rd, and ?What are the approximate values of rc, rd, and ? What is the approximate magnitude of [email protected] Lecture 12: Models of Ionic Conduction in Glass 19
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Ion Conduction in Glass: Coulombically or Structurally Constrained?Constrained? Oxide glasses, Eact ~100 kcal/mole Sulfide glasses E t ~10 kcal/mole Sulfide glasses, Eact 10 kcal/mole Eact Es Ec
Are alkali cations coulombically, Ec , constrained?y c Weak Electrolytes like HOAc, kA ~ 1 x 10-5 ? Cations are only weakly dissociated
Are alkali cations structurally E constrained? Are alkali cations structurally, Es, constrained? Strong electrolytes like NaCl? Completely dissociated, Na+ Cl- ?
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Models of the Activation Energy Both activation energies appear to be non-zero and contribute to the
total activation energy Anderson-Stuart1 model calculation
2/)( 2 dcS rrGE
2
)(12
.
ac
acstructC rr
eZZCE
x Na2O + (1-x)SiO2 Es (calc)kcal/mole
Ec (calc)kcal/mole
Eact(calc)kcal/mole
Eact2
kcal/mole11 8 11 7 66 9 78 6 68 111.8 11.7 66.9 78.6 68.119.2 10.9 62.3 73.2 63.729.7 10.0 56.1 66.1 59.7
Calculation shows that the Ec term is the larger of the two energy barriers.
Coulombically constrained?1 Anderson Stuart J Amer Cer Soc 1954
1 Anderson, Stuart, J. Amer. Cer. Soc., 19542 SciGlass 5.5, Average of many glasses
Lecture 12: Models of Ionic Conduction in Glass
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Alkali Radii Dependence of Strain and Coulomb Activation EnergiesActivation Energies
E 2
Es
Ec
(?)
?)
Ec ~ 1/rcEm ~ rc
2
A.U
.)
c
dom
inat
ed
omin
ated
(?
E s ,
E c (A
Es d
Ec d
o
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Na+H+ (?) Cs+K+
Li+
rcation ()
Lecture 12: Models of Ionic Conduction in Glass
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Strong and Weak Electrolyte models
“Strong electrolyte” model suggests allcations are equally available for conductionconduction. Each cation experiences an energy
barrier which governs the rate at which it hops
“Weak electrolyte” model suggests only those dissociated cations are available for conduction
Dissociation creates mobile carriers Dissociation creates mobile carriers available for conduction
SE models suggests that EC + Esboth contribute, one could be larger or , gsmaller than the other
WE model suggests that Ec is the dominant term
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Thermodynamic Models of Ionic Transport
Glass is considered as a solvent into which salt is dissolved
If dissolved salt dissociates strongly then glass is If dissolved salt dissociates strongly, then glass is considered a strong electrolyte
If dissolved salt dissociates weakly, then glass is considered a weak electrolyteconsidered a weak electrolyte
Coulomb energy term calculations suggest that the salts are only weakly dissociated, largest of the two energy terms
Migration energy term is taken to be minor and weaker function of compositionp
Dissociation constant then determines the number of mobile cations available for conduction, dissociation limited conductionlimited conduction
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Weak Electrolyte Model, Ravaine & Souquet ‘80
1/2M2O + SiO4/2 3/2O-Si-O-M+ 3/2O-Si-O- …… M+
(U t d) (R t d b t U di i t d) (Di i t d)(Unreacted) (Reacted but Undissociated) (Dissociated)Kdiss = aM+ aOM- / aM2O
~ [M+][OM-]/aM2O = [M+]2/ aM2O [M ][OM ]/aM2O [M ] / aM2O
[M+] ~ Kdiss1/2aM2O
1/2 n
= zen zeKdiss1/2aM2O
1/2 ~ C aM2O1/2
l K N 2RT/4 + )log Kdiss ~ -Ne2RT/4 r+ + r-)
As r+, r- increase, Kdiss increases
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As increases, Kdiss increases
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AC versus DC Ionic Conductivity
> 1
10(
a.c.)
+
|E|
0 2 4 6 8 10103K/T
2 4 6 8 10 12log10(f/Hz)
log 1
+
Ener
gy y
x
10 K/T log10(f/Hz)
+
D.C. Conductivity A.C. Conductivity
r
Charles - Polarization/Diffusion Jonscher - Universal ResponseAnderson/Stuart - Coulomb & Strain Energies Ngai - Coupling TheoryMoynihan/Macedo - Debeye & Faulkenhagen Theory Moynihan - ModulusRavaine/Souquet Weak Electrolyte Dyre Power Law
Lecture 12: Models of Ionic Conduction in Glass 26
Ravaine/Souquet - Weak Electrolyte Dyre - Power LawMalugani- AgI Micro domains Funke - Jump Relaxation
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AC ionic Conductivity in Glass
Connection to Far-IR vibrational modes Angell ‘83
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