Advanced Vitreous State - Physical Properties of Glass Lecture 26: - - PowerPoint PPT Presentation

Advanced Vitreous State - Physical Properties of Glass

Lecture 26: Charge Conduction Properties of Glass: Ionic Conduction in Glass - Part 2 Activation Energies in Glass Steve W. Martin

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

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 glasses is still very low except for the highest temperatures

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

DC ion conductivity in glass

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

• xygens

“Mobile” lithium ions The higher the

concentration of Li2O, the higher the conductivity higher the conductivity

Lower resistivity

Activation energy

decreases with Li2O content

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 3

Composition Dependence of the Conductivity

• Binary lithium phosphate

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

Li2O+ B2O3 Li2O+ SiO2 50 oC

relative poor ion conductors

• Binary lithium borate glasses,

Li2O + B2O3, are slightly better d t

Li2O+ P2O5 T = 15

conductors

• Binary lithium silicate glasses,

Li2O + SiO2 are slightly better d t t

Li2O+ P2O5

conductors yet.

Li2O:P2O5 Li2O:SiO

2

Li2O:B2O3

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 4

Salt doped phosphate glasses

• Halide doping strongly

increases the conductivity

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 5

Salt doped phosphate glasses

• Halide doping strongly

increases the conductivity

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 6

Effect of Sulfur Substitution – “Fast Ion Conductors”

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 7

Silver Phosphate Glasses

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 8

Other Silver sulfide doped glasses

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 9

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 10

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 11

0.0 0.2 0.4 0.6 0.8 1.0

Composition (x)

Composition Dependence of the Conductivity

• Binary lithium phosphate

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

Li2O+ B2O3 Li2O+ SiO2 50 oC

relative poor ion conductors

• Binary lithium borate glasses,

Li2O + B2O3, are slightly better d t

Li2O+ P2O5 T = 15

conductors

• Binary lithium silicate glasses,

Li2O + SiO2 are slightly better d t t

Li2O+ P2O5

conductors yet.

Li2O:P2O5 Li2O:SiO

2

Li2O:B2O3

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 12

Ionic motion in glassy electrolytes

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

+ + +

MD Simulations

|E|

+ + + + +

y x

BO

+ +

ΔEact = ΔΕs + ΔEc

ergy

• +

NBO NBO BO

• +

+1/rn

ΔEs = Strain Energy ΔEc = Coulomb Energy

act s

c

Ene

r r

ΔEC ΔES

• e2/r

swmartin@iastate.edu 13

S.W. Martin, C.A. Angell, JNCS, 1983

Ionic Conduction in Glass – Part 2

Mobility and number dependence of the conductivity

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ − = = RT E T T eZ T n T

act c

exp ) ( ) ( ) ( σ μ σ ⎠ ⎝ RT T

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ − = RT E n T n

c

• exp

) ( ⎠ ⎝ RT ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ − = E T

s

exp ) ( μ μ ⎟ ⎠ ⎜ ⎝ RT T p ) ( μ

( )⎞

⎛ Δ Δ E E Z

Question: What are the magnitudes of ΔE and ΔE ?

( )⎟

⎠ ⎞ ⎜ ⎝ ⎛ Δ + Δ − = RT E E T en Z T

s c c

exp ) (

0μ

σ

swmartin@iastate.edu 14

Question: What are the magnitudes of ΔES(M) and ΔEC ?

Ionic Conduction in Glass – Part 2

“Extreme” Models of the Activation Energy

Strong Electrolyte Model

All cations are dissociated from their “host” anion and are

available for conduction available for conduction

• Like NaCl, HCl, NaOH, H2SO4 dissolved in water

Na+….-O-Si≡ ΔEC is “small” and not strongly compositionally dependent σd.c. ~ Zen0μ0/T exp(- ΔEm/RT)

Mi ti d i t th d d ti it

Migration energy dominates the d.c. conductivity

swmartin@iastate.edu 15 Ionic Conduction in Glass – Part 2

“Extreme” Models of the Activation Energy

Weak Electrolyte Model

Only a small fraction of the cations are dissociated

Lik HOAC A ti A id K 1 8 10 5

• Like HOAC, Acetic Acid, Ka ~ 1.8 x 10-5

ΔEm is “small” and not strongly compositionally

dependent dependent

Most of the cations are bound with their charge

compensating anion / ( / )

σd.c. ~ Zeμ0n0/T exp(- ΔEc/RT) Creation energy dominates the d.c. conductivity

swmartin@iastate.edu 16 Ionic Conduction in Glass – Part 2

Strong and Weak Electrolyte models

• “Strong electrolyte” SE model

suggests all cations are equally available for conduction available for conduction.

• Each cation experiences an energy

barrier which governs the rate at which it hops

• “Weak electrolyte” WE 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 ΔEC + ΔEs

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

• WE model suggests that ΔEc is the

dominant term

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 17 S.W. Martin, C.A. Angell, JNCS, 1983

Coulomb Energy Barrier

Anderson-Stuart Model Assignment of Coulombic and Strain energy terms 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 2 18

. ) ( const r r E Lim

a c act

+ → Δ

∞ ∞ →

ε

λ

Strain Energy Barrier

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

2

gy 30 40 50 mole)

G Shear modulus rc Cation radius rd Interstitial site radius

10 20 30 ΔEs(kcal/m d

λ Jump distance

0.04 0.08 0.12 0.16 0.2

Cation Radius (nm) swmartin@iastate.edu Ionic Conduction in Glass – Part 2 19

Cation Radius Dependence of ΔEc and ΔEm

ΔEs

ΔE

ΔEc ~ 1/rc ΔEs ~ rc

2

(A.U.)

ΔEc

ΔEtot dominated

• minated

ΔEs , ΔEc

ΔEs d ΔEc d 0.0 0.5 1.0 1.5 2.0 2.5 3.0

• Na

+

H

+ (?)

Cs

+

K

+

Li

+

( )

swmartin@iastate.edu 20

rcation (Α)

Ionic Conduction in Glass – Part 2

“Rational” Models of the Activation Energy

• Both activation energies are non-zero and contribute to the total

activation energy

• Anderson-Stuart1 model calculation

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + = Δ

∞

λ ε β 2 ) ( 1

2 . a c a c struct C

r r e Z Z E

2

) ( 4

d c d m s

r r G r E E − = Δ = Δ π

x Na2O + (1-x)SiO2 ΔEs (calc) ΔEc (calc) ΔEact(calc) ΔEact

2

11.8 11.7 66.9 78.6 68.1 19 2 10 9 62 3 73 2 63 7

• Calculation shows that the ΔEc term is the larger of the two energy

19.2 10.9 62.3 73.2 63.7 29.7 10.0 56.1 66.1 59.7

• Calculation shows that the ΔEc term is the larger of the two energy

barriers.

• Weak-Electrolyte behavior?

1 Anderson, Stuart, J. Amer. Cer. Soc., 1954 2 SciGlass 5.5, Average of many glasses

swmartin@iastate.edu 21

SciGlass 5.5, Average of many glasses

Ionic Conduction in Glass – Part 2

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 2 22

Weak Electrolyte model, Ravaine & Souquet ‘80

1/2M2O + SiO4/2

3/2O-Si-O-M+

• 3/2O-Si-O- …… M+

(Unreacted) (Reacted but Undissociated) (Dissociated) (Unreacted) (Reacted but Undissociated) (Dissociated) Kdiss = aM+ aOM- / aM2O

~ [M+][OM-]/aM2O = [M+]2/ aM2O

[M+] ~ Kdiss

1/2aM2O 1/2 ≡ n

σ = zeμn = zeμK

1/2a 1/2 ~ C a 1/2

σ = zeμn = zeμKdiss aM2O ~ C aM2O log Kdiss ~ -Ne2RT/4πεοε∞ (r+ + r-) As r+, r- increase, Kdiss increases As ε∞ increases, Kdiss increases

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 23

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 24

Intermediate Range Order models

• Cluster pathway model,

Greeves et al ‘85

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 25

Conductivity percolation in AgI + AgPO3

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 26

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 27

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 28

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 2 29

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 2 30

AgI Microdomain model

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 31

Part 2 Summary

Conductivity can be increased many orders

• f magnitude

Essentially insulating values 10-15 (Ωcm)-1 “High Conducting” values 10-2 (Ωcm)-1 Activation energy appears to be dominated by

coulomb potential

Weakening the coulomb potential between cation

and anion lowers the activation energy

Oxide glasses lowest conducting Oxide glasses lowest conducting Sulfide glasses doped with ionic salts the highest

conducting

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 33

AC ionic conductivity in glass

Connection to Far-IR vibrational modes,

Angell ‘83 Angell 83

swmartin@iastate.edu Ionic Conduction in Glass – Part 2 34