[PPT] - Advanced Vitreous State - Physical Properties of Glass Lecture 25: PowerPoint Presentation

SLIDE 1

Advanced Vitreous State - Physical Properties of Glass

Lecture 25: Charge Conduction Properties of Glass: Ionic Conduction in Glass - Part 1 Relationship to Glass Structure and Composition p

Steve W. Martin

Department of Materials Science & Engineering Iowa State University Ames, IA swmartin@iastate.edu

SLIDE 2

Ionic Conduction in glass

Glasses can be systematically doped to increase

conductivity

From near insulating values to those that rival ionic liquids

Strong glass forming character over wide compositions

ranges make them ideal for man composition st dies of ranges make them ideal for many composition studies of the ionic conductivity

Low melting temperatures often make them compatible

g p p with many industrial processing techniques such as sputtering and evaporation to produce thin film electrolytes electrolytes

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 2

SLIDE 3

Formation of Non-Bridging Oxygens

Modifier M2O or MO creates two NBOs per M2O or MO added
xNa2O + (1-x)SiO2 creates 2x NBOs

f NBO /(NBO + BO )

fNBO = NBOs/(NBOs + BOs)

= 2x/(x + 2(1-x)) = 2x/(2-x)

fBO = 1- fNBO

Q4 Q4 Q3 Q3

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 3

SLIDE 4

“Qi” Units in Alkali Silicate Glasses

Q4 Q2 Q3 O Si Q0 Q1 Na+

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SLIDE 5

Alkali Ions are “weakly” bound

“Frame work” cations, Si+4, and anions, O=

Covalently bonded to the network

“Large” bond strength 100+ kcal/mole

Large bond strength, 100+ kcal/mole

“Modifying” cations, M+ , and anions F-

Ionically bonded to the network “Small” bond strength, < 50 kcal/mole

Alkali cations can be thermally activated

T b k th i k i i b d

To break their weak ionic bond And move from one alkali cation site to another Thermally activated ionic conduction Thermally activated ionic conduction….

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 5

SLIDE 6

Relation of glass structure to ionic conduction

xNa2O + (1-x)SiO2 Glass in 2-D

+ +

|E|

+ + + + + + +

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SLIDE 7

Molecular Dynamics Simulation of Ionic Conduction

Go to Movie…..

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SLIDE 8

Relation of glass structure to ionic conduction

BO

+

NBO NBO BO

+

ΔEact = ΔΕs + ΔEc

nergy BO +1/rn

ΔEs = Strain Energy ΔEc = Coulomb Energy

En ΔEC ΔES

e2/r

r r

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 8

SLIDE 9

Cation Conduction – “Rattle and Jump”

BO

+

NBO NBO BO

gy

BO +1/rn

MD Simulations

Energ ΔE ΔES y

r r

ΔEC

e2/r

x

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 9

SLIDE 10

Theory of Ionic Conduction in Glass: Simple Models

σ = 1/ρ ≡ neZμ

n is the number density

eZ is the charge +1 most of

eZ is the charge, +1 most of

the time

μ is the mobility

What are the units of n?

#/cm3

What are the units of μ? What are the units of μ?

(cm/sec)/V = cm/V-sec

What are the units of σ?

(Ω cm)-1 ≡ S/cm swmartin@iastate.edu Ionic Conduction in Glass – Part 1 10

SLIDE 11

Theory of Ionic Conduction in Glass: Simple Models

E ze λ

→

2

→

E

2 E ze Eact λ − Δ

λ

2

+

λ λ/2

|E|

+ + + + + + swmartin@iastate.edu Ionic Conduction in Glass – Part 1 11 + +

SLIDE 12

Theory of Ionic Conduction in Glass: Simple Models

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − Δ − =

+

RT E ze E T

act

2 / exp ) ( λ υ υ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + Δ − = ⎦ ⎣

−

RT E ze E T RT

act

2 / exp ) ( λ υ υ ⎞ ⎛ ⎤ ⎡ ⎤ ⎡ − = ⎥ ⎦ ⎢ ⎣

− +

T T RT

net

) ( ) ( υ υ υ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡− − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = RT E ze RT E ze RT Eact

net

2 exp 2 exp exp λ λ υ υ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = RT E RT E ze RT E ze RT E

act act net

exp ~ 2 sinh exp 2 λ υ λ υ υ

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 12

⎠ ⎝

SLIDE 13

Theory of Ionic Conduction in Glass: Simple Models

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − ⎟ ⎟ ⎞ ⎜ ⎜ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = E E ze E ze E

act act net

exp ~ sinh exp 2 λ υ λ υ υ ⎥ ⎤ ⎢ ⎡ Δ − = × = ⎥ ⎦ ⎢ ⎣ ⎟ ⎠ ⎜ ⎝ ⎥ ⎦ ⎢ ⎣ E E ze velocity RT RT RT RT

act net

exp p 2 p

2

λ υ λ υ ⎥ ⎤ ⎢ ⎡ Δ = = ⎥ ⎦ ⎢ ⎣ − = × = E ze E velocity mobility RT RT velocity

act net

exp / exp

2 0λ

υ λ υ × × = ⎥ ⎦ ⎢ ⎣ − = = charge ty conductivi mobility ty conductivi RT RT E velocity mobility exp /

( )

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − ≡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = RT E T RT E RT ze n (T)

act act

exp exp

2 2

σ λ υ σ

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 13

SLIDE 14

Theory of Ionic Conduction in Glass: Simple Models

ΔEs = Strain Energy ΔEact = ΔΕs + ΔEc

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = RT E T (T)

act

exp σ σ

s

ΔEc = Coulomb Energy

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + Δ − = ⎦ ⎣ RT E E T

S C

exp σ

+

NB NBO BO

+

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = ⎦ ⎣ RT E n T n

C

exp ) (

nergy

+

NB O NBO BO

+

+1/rn

= ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − = ⎦ ⎣ RT E T T

S

exp ) ( μ μ

En ΔEC ΔES

e2/r

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ − ⎦ ⎣ RT E RT ze

S

exp ) (

2 2 0λ

ν

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 14

r r

⎦ ⎣

SLIDE 15

Arrhenius Ionic Conductivity in Glass

00 00 00 00

10

10

1

160 140 120 100 800 600 400 200

Temperature (

C)

Glassy Crystalline Tg Tm

α-AgI

10

1

10

RbAg

4

I

5

2 9 . 8 A g

2

O

4

. 4 ( A g I ) 2 9

β-NaAl11O17

3 5 L i O Zr

m)

1

10

3

10

2

g I )

2

2

9 . 8 P

2

O

5

2 8 . 6 A g

2

O

4

2 . 8 ( A g I )

2

2

8 . 6 M

O

3

50Ag2S-5GeS-45GeS i

2

O

3

L i

2

S O

4

1

( L i C l ) L i

4

B

7

O

1 2

C l 2 6 . 9 L i

25Li2O-25A

ZrO2-9%Y2O3

σdc (Ω-cm

5

10

4

GeS2 )

2

1

2 . 5 S i O

2

1

2 . 5 B

2

O

3

L i

2

O

9

( L i C l )

2

6

4 . 1 B

2

O

3

LiAlSiO4

Al2O3-50SiO2

25Li2O -75B2O LiNbO3

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 10

6

10

5

3 3 4 2O3

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

1000 / T (K

1)

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 15

SLIDE 16

Binary Alkali Silicate Glasses

Addition of Na2O Increases

the ionic conductivity, y, decreases the electrical resistivity Increasing the temperat re

Increasing the temperature

increases the ionic conductivity, decreases the ionic resistivity

Ionic conductivity of soda

glasses is still very low except glasses is still very low except for the highest temperatures

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 16

SLIDE 17

DC ion conductivity in glass

xLi2O + (1-x)P2O5
Creation of non-

Bridging oxygens

“Mobile” lithium ions
The higher the

g concentration of Li2O, the higher the conductivity

Lower resistivity
Activation energy

decreases with Li2O content

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 17

SLIDE 18

Composition Dependence of the Conductivity

Binary lithium phosphate

glasses, Li2O + P2O5, are l ti i d t

Li2O+ B2O3 Li2O+ SiO2

relative poor ion conductors

Binary lithium borate glasses,

Li2O + B2O3, are slightly better d t

Li O+ P O

conductors

Binary lithium silicate glasses,

Li2O + SiO2 are slightly better d t t

Li2O+ P2O5

conductors yet.

Li2O:P2O5 Li2O:SiO2 Li2O:B2O3

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 18

SLIDE 19

Salt doped phosphate glasses

Halide doping strongly

increases the conductivity

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SLIDE 20

Effect of Sulfur Substitution

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SLIDE 21

Salt doped phosphate glasses

LiI doped LiPO3 show highest conductivity and lowest activation

energy among the halides

Crystallization at the end of the glass forming limit

T = 298 K

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SLIDE 22

Silver Phosphate Glasses

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SLIDE 23

Other Silver sulfide doped glasses

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SLIDE 24

Mixed Glassformer Systems

Phosphate and borate mi ed glasses sho non linear “Mi ed

Phosphate and borate mixed glasses show non-linear “Mixed

Glassformer” effect

Conductivity and Activation Energies in 0 65N S 0 35[ B S (1 )P S ]

22 23 4.0x10

5

5.0x10

5

0.65Na2S + 0.35[xB2S3+ (1-x)P2S5]

Conductivity

20 21 3.0x10

5

/mol) at 25

C

18 19 1.0x10

5

2.0x10

5

ΔEact (kJ σd.c. (S/cm) a

0 0 0 2 0 4 0 6 0 8 1 0 17 18 0.0

Activation Energy

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0.0 0.2 0.4 0.6 0.8 1.0

Composition (x)

SLIDE 25

Short Range Order models of Conduction Energetics

Anderson-Stuart Model Assignment of Coulombic and Strain energy terms ΔEC + Assignment of Coulombic and Strain energy terms, ΔEC +

ΔEs

“Creation” or Concentration versus Migration energy

terms, ΔEC + ΔEm

Coulomb energy term, ΔEC attractive force between

cation and anion cation and anion

2 ) ( 1 ) ( 2 /

2 . 2 2 .

r r e Z Z C r r e Z Z e Z Z C

a c struct a c a c struct

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − − − ≈ λ ε λ ε . ) ( ) ( 2 /

2 .

const e Z Z C E Lim r r r r

a c struct t a c a c

= → Δ ⎦ ⎣ + ⎦ ⎣ +

∞ ∞

λ ε λ ε

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 25

. ) ( const r r E Lim

a c act

+ → Δ

∞ ∞ →

ε

λ

SLIDE 26

Short Range Order models

Strain energy term - ΔEs “Work” required to “dilate the network so large cations

i t can migrate

Cation size affect on Strain Energy

ΔE G r r

S c d

= − π λ ( ) /

2

gy 30 40 50 mole)

G Shear modulus rc Cation radius

10 20 30 ΔEs(kcal/m

rd Interstitial site radius λ Jump distance

0.04 0.08 0.12 0.16 0.2

Cation Radius (nm) swmartin@iastate.edu Ionic Conduction in Glass – Part 1 26

SLIDE 27

Thermodynamic Models

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 dissociate weakly, then glass is

considered a weak electrolyte considered 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 weak

function of composition p

Dissociation constant then determines the number of

mobile cations available for conduction, dissociation limited conduction limited conduction

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 27

SLIDE 28

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+] ~ Kdiss

1/2aM2O 1/2 ≡ n

σ = zeμn = zeμKdiss

1/2aM2O 1/2 ~ C aM2O 1/2

l K N 2RT/4 ( + ) log Kdiss ~ -Ne2RT/4πεοε∞ (r+ + r-) As r+, r- increase, Kdiss increases

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 28

As ε∞ increases, Kdiss increases

SLIDE 29

Strong and Weak Electrolyte models

“Strong electrolyte” model suggests all

cations are equally available for conduction conduction.

Each cation experiences an energy

barrier which governs the rate at which it hops

“Weak electrolyte” model suggests
nly those dissociated cations are

available for conduction

Dissociation creates mobile carriers

Dissociation creates mobile carriers

available for conduction

SE models suggests that ΔEC + ΔEs

both contribute, one could be larger or , g smaller than the other

WE model suggests that ΔEc is the

dominant term

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SLIDE 30

Intermediate Range Order models

Models recognize that ion conductivity requires ion

motion over relatively long length scales I t b bl t f id f th

Ions must be able to move from one side of the

electrolyte to the other

Long range connectivity of the SRO structures favorable

Long range connectivity of the SRO structures favorable to conduction must exist

Deep “traps” along the way must be infrequent and not

severe

Rather, low energy conduction “pathways” are thought to

exist which maximize connectivity and minimize energy exist which maximize connectivity and minimize energy barriers and traps

Cluster pathway model of Greeves ‘85, for example

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SLIDE 31

Intermediate Range Order models

Cluster pathway model,

Greeves et al ‘85

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SLIDE 32

AC versus DC ionic conductivity

ωτ > 1 ωτ < 1

g10(σa.c.)

+

gy

y

0 2 4 6 8 10 103K/T 2 4 6 8 10 12 log10(f/Hz) lo +

Energ

r

y x

+

D.C. Conductivity A.C. Conductivity

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SLIDE 33

AC ionic conductivity in glass

Connection to Far-IR vibrational modes,

Angell ‘83 Angell 83

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SLIDE 34

Intermediate Range Order models

Percolation Models - Johari et al. ‘87

At low dopant concentrations
At low dopant concentrations
Cations are far separated
Mobile species are diluted in a non-conducting host glass
At intermediate concentrations
At intermediate concentrations
Cations begin to approach proximity
Preferential conduction paths form
Sites percolate
Sites percolate
At high concentrations
Cations are fully connected
Conduction pathways are fully developed
Conduction pathways are fully developed

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 34

SLIDE 35

Conductivity percolation in AgI + AgPO3

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SLIDE 36

RMC Modeling of AgI + AgPO3, Swenson et al. ‘98

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SLIDE 37

Intermediate Range Order models

Microdomain models of conductivity Dopant salts such as AgI to oxide glasses especially Dopant salts such as AgI to oxide glasses, especially

AgPO3, are added to increase conductivity

AgI is itself a FIC crystal above 150oC Extrapolations of σ to xAgI = 1 give ~ σAgI(298K) The question then is: Does the AgI create “microdomains”

f α AgI giving rise to the high conductivity?
f α-AgI giving rise to the high conductivity?

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 37

SLIDE 38

AgI Microdomain model

Most well known of all glasses is xAgI + (1-x)AgPO3 AgPO3 is a long chain structure of -O-P(O)(OAg)-O

t it repeat units

Intermediate range structure is for these long chains to

intertwine and as such frustrate crystallization intertwine and as such frustrate crystallization

Added AgI dissolves into this liquid without disrupting the

structure of the phosphate chains

Microdomain model then suggests that this dissolved AgI

creates increasingly large clusters of α-AgI between the phosphate chains phosphate chains

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 38

SLIDE 39

AgI Microdomain model

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 39

SLIDE 40

Ionic Conduction in Glass

Ohms law

V = IR

A

V = IR V = I ρ t/A = I ρ k ρ = 1/σ

t

ρ

1/σ

ρ(Ωcm), σ(Ωcm)-1

Calculate σ for

I = 1 μA V = 1 V k = 1 mm/1 cm2

swmartin@iastate.edu Ionic Conduction in Glass – Part 1 40