Advanced Vitreous State - Physical Properties of Glass Lecture 27: - - PowerPoint PPT Presentation

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Advanced Vitreous State - Physical Properties of Glass Lecture 27: - - PowerPoint PPT Presentation

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Advanced Vitreous State - Physical Properties of Glass Lecture 27: Charge Conduction Properties of Glass: Ionic Conduction in Glass - Part 3 Intermediate Range Order Models and Effects of Frequency Steve W. Martin Department of Materials

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SLIDE 1

Advanced Vitreous State - Physical Properties of Glass

Lecture 27: Charge Conduction Properties of Glass: Ionic Conduction in Glass - Part 3 Intermediate Range Order Models and Effects of Frequency Steve W. Martin

Department of Materials Science & Engineering Iowa State University Ames, IA swmartin@iastate.edu swmartin@iastate.edu 1 Ionic Conduction in Glass – Part 3

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SLIDE 2

swmartin@iastate.edu 2

Activation Energies of Ionic motion in glassy electrolytes

Es = Strain Energy Ec = Coulomb Energy Eact

s

Ec

y x

MD Simulations

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

Energy

  • +

|E|

NBO NBO BO BO

r r

  • +

+ + + + + + + + EC ES

  • e2/r

+1/rn

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

Ionic Conduction in Glass – Part 3

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SLIDE 3

swmartin@iastate.edu 3

Cation Radius Dependence of Ec and Em

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • Na

+

Es dominated Ec dominated

Ec ~ 1/rc Es ~ rc

2

H

+ (?)

Cs

+

K

+

Li

+

Es , Ec (A.U.) rcation ( )

Es Ec Etot

Ionic Conduction in Glass – Part 2

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SLIDE 4

swmartin@iastate.edu 4

“Rational” Models of the Activation Energy

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

Anderson-Stuart1 model calculation

Calculation shows that the Ec 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

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

x Na2O + (1-x)SiO2 Es (calc) Ec (calc) Eact(calc) Eact

2

11.8 11.7 66.9 78.6 68.1 19.2 10.9 62.3 73.2 63.7 29.7 10.0 56.1 66.1 59.7

Ionic Conduction in Glass – Part 3

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Thermodynamic Models

 Glass is considered as a solvent into which salt is

dissolved

 If dissolved salt dissociates strongly, then glass is

considered a strong electrolyte

 If dissolved salt dissociate weakly, then glass is

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

 Dissociation constant then determines the number of

mobile cations available for conduction, dissociation limited conduction

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 5

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Weak Electrolyte model, Ravaine & Souquet ‘80

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 6

1/2M2O + SiO4/2 

3/2O-Si-O-M+

3/2O-Si-O- …… M+

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

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

[M+] ~ Kdiss

1/2aM2O 1/2

n = ze n ze Kdiss

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

log Kdiss ~ -Ne2RT/4 r+ + r-) As r+, r- increase, Kdiss increases As increases, Kdiss increases

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SLIDE 7

Intermediate Range Order models

Models recognize that ion conductivity requires ion motion over relatively long length scales

Ions must be able to move from one side of the electrolyte to the

  • ther

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 barriers and traps

Cluster pathway model of Greeves „85, for example

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 7

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SLIDE 8

Intermediate Range Order models

Cluster pathway model, Greeves et al ’85

Ionic structures in the glass group

Covalent structures in the glass group

This forms regions of high NBO concentration

Causes conductivity to increase faster than simple uniform mixing would suggest

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 8

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SLIDE 9

Conductivity percolation

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 9

http://www.tda.com/eMatls/images/Composites/percolation_scheme.gif http://www.physics.upenn.edu/yodhlab/images/research_CMP_percolation_plot.jpg

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Conductivity percolation in AgI + AgPO3

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 10

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

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 11

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Intermediate Range Order models

 Microdomain models of conductivity  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

to xAgI = 1 give ~

AgI(298K)  The question then is: Does the AgI create “microdomains”

  • f -AgI giving rise to the high conductivity?

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 12

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SLIDE 13

AgI Micro-domain model

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

repeat units

 Intermediate range structure is for these long chains to

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 -AgI between the phosphate chains

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 13

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SLIDE 14

AgI Micro-domain model

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 14

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Ionic Conduction in Glass – Part 3 15

AC versus DC ionic conductivity

D.C. Conductivity

A.C. Conductivity

Anderson/Stuart - Coulomb & Strain Energies Ngai - Coupling Theory Moynihan/Macedo - Debeye & Faulkenhagen Theory Moynihan - Modulus Ravaine/Souquet - Weak Electrolyte Dyre - Power Law Malugani- AgI Micro domains Funke - Jump Relaxation

> 1 Energy

r

y x

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

a.c.)

+

+

+

|E|

swmartin@iastate.edu

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Ionic Conduction in Glass – Part 3 16

AC ionic conductivity in glass

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Ionic Conduction in Glass – Part 3 17

AC ionic conductivity in glass

 AC Conductivity in Glass

0.05K2S + 0.95B2S3

swmartin@iastate.edu

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SLIDE 18

AC ionic conductivity in glass

 Connection to Far-IR vibrational modes,

Angell ‘83

swmartin@iastate.edu Ionic Conduction in Glass – Part 3 18

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SLIDE 19

Ionic Conduction in Glass – Part 3 19

AC ionic conductivity in glass

0.56Li2S + 0.44SiS2 FIC glass

 NMR = 0.35

=0.48

Eact = 8.94 kcal/mol (7.95)

 0NMR = 4.5 x 10-14secs  0 = 4 x 10-15 

What is the origin of the difference in

NMR and

?

Why are the activation energies also different?

Why are the pre-exponential factors different by a factor of 10?

 Relationships between NMR and AC conductivity measurements

swmartin@iastate.edu

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SLIDE 20

Ionic Conduction in Glass – Part 3 20

AC ionic conductivity in glass

 Average relaxation times

 For Conductivity and NSLR

are:

 Different in magnitude  Different in temperature

dependence

 What is the origin of the

differences?

 Sigma and NSLR

completely different processes?

 Is there a consistent

formalism to treat both sets of data?

swmartin@iastate.edu

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SLIDE 21

Ionic Conduction in Glass – Part 3 21

AC ionic conductivity in glass - DAEs Treatment

 Our fundamental hypotheses are that:

 Mobile ions reside in a disordered structure which create:  Variations in coordination number  Variations in bond lengths  Variations in bond strengths  Variations in jump distances to next cation site, which therefore  Create variations in activation energies from cation to cation in the

glass

 The distribution is hypothesized to be: 

Continuous

Discrete

Centered about a mean

Symmetric to low and high energy values

swmartin@iastate.edu

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SLIDE 22

Ionic Conduction in Glass – Part 3 22

AC ionic conductivity in glass - DAEs Treatment

Using a DAEs to treat ion conduction in glass is not new

Von Schweidler used a DRTs as early as 1907

  • Ann. Physik. 24(1907)711.

Cole and Cole, Cole and Davidson reported log Guassian DAEs

  • J. Chem. Phys. 9(1941) 341

  • H. E. Taylor used a DAEs to describe the dielectric relaxation

Modeling ‟ and ” in soda-lime-silicate glass in 1955

  • Trans. Fara. Soc. 51(1955)873.

  • C. T. Moynihan used a log Guassian treatment

Modeling conductivity relaxation in CKN melts and glasses in 1972

  • Phys. Chem. Glasses 13(1972)171

swmartin@iastate.edu

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SLIDE 23

Ionic Conduction in Glass – Part 3 23

Determination of the DAEs in Glass

 Direct measurement

through NMR NSLR data

 Conduction process is by

the percolation through low barrier sites

 Conductivity will only

measure the low energy barriers

 NSLR measures all

cations, both contribute to NSLR T1

Glassy FIC

Crystalline FIC Stevels & Taylor DAEs model,

swmartin@iastate.edu

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SLIDE 24

Ionic Conduction in Glass – Part 3 24

NMR NSLR Data

 Determination of the DAEs from NSLR T1 measurements

NMR NMR a L a a L a L L

dE Z C T R T T

2 2 2 2 1 1

4 1 4 1 ) , ( ) , ( / 1

2 2 1 1 2 2 2

) ( 1 2 exp 2 1 ) 1 ( ) (

a m b a m b a NMR

E E E E y E E E E y E Z

 Gaussian DAEs with Lorentzian “tail”, y ~ 0.2, to account for low temperature,

high frequency “extra” relaxation

swmartin@iastate.edu

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SLIDE 25

Ionic Conduction in Glass – Part 3 25

DAEs from FIC Li2S + GeS2 Glasses

swmartin@iastate.edu

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SLIDE 26

Ionic Conduction in Glass – Part 3 26

DAEs from FIC Li2S + GeS2 Glasses

 Average of distribution

shifts to smaller activation energies with increasing Li2S

 Distribution does not

change shape significantly, all have ~ same FWHM

 0.55 Glass is slightly

narrower

swmartin@iastate.edu

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SLIDE 27

Ionic Conduction in Glass – Part 3

27

Modeling of the DC conductivity from DAE (NSLR)

 DC = NPe2d2/6kBT av 

ra = roaexp(-Ea/RT)

roa = Em/2m)1/2/d

 a = 1/6ra, assuming an

  • ctahedral site

  • a = 2.7 x 10-12/(Em/kB)1/2

a a NMR a E a

dE E Z T E P

P

) ( ) / ( ) / 1 (

av

swmartin@iastate.edu

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SLIDE 28

Ionic Conduction in Glass – Part 3 28

Modeling of the AC Conductivity

CTRW approximation of the AC conductivity

 Dyre et al

i T E i T

a a dc

) , ( / 1 / ) , ( 1

a a

E a a NMR E a a NMR a a a a

dE E Z dE E Z T E T E

' ' ' ' '

) ( ) ( ) , ( ) , ( 1

KWW

swmartin@iastate.edu

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SLIDE 29

Ionic Conduction in Glass – Part 3 29

Multiple FIC Dynamics in Glass

“Multiple Channel” ion relaxation in FIC glasses

R1 data show evidence of multiple relaxation processes

Fast process at low T, slower process at higher T

Alkali thioborate glasses are speciated into tetrahedral borons and trigonal borons with NBS

Are “slow” Li+ ions associated with NBS?

Are “faster” Li+ ions associate with BS4/2

  • groups?

swmartin@iastate.edu

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SLIDE 30

Ionic Conduction in Glass – Part 3 30

Multiple FIC Dynamics in Glass

Relaxation spectra of both mobile Li+ ions and immobile frame work B ions were measured

Multiple-channel relaxation was

  • bserved for Li+ ions

BS3 and BS4 units have different relaxation rates and hence difference DAEs to characterize their dynamics

N4 of 0.7Li2S is 0.05

Most Li+ ions are associated with BS3

3- groups, as

evidenced in the DAEs

swmartin@iastate.edu

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SLIDE 31

Ionic Conduction in Glass – Part 3 31

Summary – Part 3

 The DAEs is an established formalism  Reflects intrinsic disorder of glass  In principle is a “calculable” property of glass once

structure is known

 Accurately predicts (models) a variety of dynamic data,

conductivity and NSLR

 “Naturally” treats multiple relaxation spectra  Accurately models DC and AC conductivity data

swmartin@iastate.edu