Ionic diffusion and frequency dependent conductivity in amor-phous materials

Journal ol Non.CrysuUine North-l-lollwJ, Amskrdam

Solids 90 (1987)

421

IONIC PHOUS

DIFFUSION MATERIAL5

Hanno

KAHNTand

Department GDR

421 .4?4

AND

FREQUENCY

DEPENIIEX'I'

CONDUCTIVITY

IN

AMOR-

FalkSCIiIFtRMEXS'IY3R

of

Chemistry,

Friedrioh

Sohiller

University,

Jena,

The "universal" frequenoy dependence of conductivity that is known from disordered electronic systems is observed for ionio oonduoting glasses too. Variation of ohemioal oomposition does not influence this behaviour. The diffusion ooefficient oaloulated from dc-oonduotivity exoeeds the diffusion coefficient obtained from traoer diffusion studies indicating correlated oarrier motion. These results euggeet that the power law frequency dependence of oonductivity is connected with iuteraotions between hopping ions. 1.

l3TRODUCTION The ac-oonduotivity

show

a power

of

law

Re G(w)

as

a common

type of lished'. tistical (CTRW) to any nature tion

for a variety general

of hopping transport function W(t). TfLis

is

the

frequency D(iu)

a wide

olass

0 Elsevier Publishing

known

to

=

$

materials.

introduoing function is of hopping One of the diffusion -

For

approaohes that starts

is

this eatabfrom sta-

Time Random Walk approach Thin model is not restrioted considers only the stoohaetio

iw*(iw) ~ I-Jl(iw)

an event time distribuobtained from a oonfiguratime maiu

distributions results

in of

this

the mo-

aoefficient

(2)

displacement of the diffusing partioles $(iu) the of frequenoy and with event time distribution funotion JI (t). Nernst-Einetein relation one obtains the

oonduotivity

Physics

ie

(1)

of

of theoretical mioroscopio model

dependent

with A* the meen square which is nearly independent Laplaoe transform of the Combining eq. 2 with the

0022-3093/87/$03.50 (North-Holland

systems

O
averagein& prooedure under consideration.

system

del

bin

meohanics is the Contiuous developed by Soher and Lax2. special type of hopping but

tional

hopping

dependence

-

behaviour

transport A quite

eleotronic

frequency

Science Publishers Division)

B.V.

G

e2 N

(iw)

= k~

A2

'-

.

6

with

N the

concentration

Boltzmann Originally, systems. port in sical 2.

constant

of end

the

hopping

over

EXPERIMENTAL Starting from

e the

elementary

T the temperature. "as applied to

CTRV

Neverless it ionic conduoting

ions,

iu*(i,) ~ 1-*(iw)

can

equally solids

an

energy

simple

Na-

oharge,

electronic

be used considering

to

k

the

conducting

study ionic

hopping motion

as

transclas-

barrier.

end

K-silicate

glasses

with

the

oom-

position M = Na,

G 1: (~‘-‘),4S~‘32)~,.3 a part of the Si02 was nent mixture to inorease compositions

substituted disorder

by in

(M20)

and

G

(~O),~.~(S~O2)75~~(~~0)~~o(PbO),~g(As203),~O(As203)0~,

The

composition

18.@io2),4.

of

conoentration tracer diffusion measurement ly. Details

n =

a multioomporesultant

The

was

l(B203)7.4

all

glasses

constant ooeffioient

and by of the

was

chosen

?..9 * 102' have been

the residue measuring

radio procedures

so

0.65.

1). From the was oaloulated of conduotivity

G(w)

=

G(0)

and

G(O)

[

1 +

T depend

the

Conductivity determFned by

aotivity are temperature

alkali and admittance

method respeotive3 . given elsewhere and the kind of frequency

(iwr)"

on

that

am-3.

Indendent of chemical composition, alkali ion all samples confirm the "universal" denoe given by the empirical equation

with

by

are

G 2: =:

B 0 or 2 3 the system.

K

depen-

]

(4)

oomposition

and

temperature

(fig.

was

do-oonduotivity G(O) the using the Nernst-Einstein measurements the traoer

determined

diffusion. ooeffioient

representing In

all glasses exceeds the

the

statio

investigated tracer diffusion

diffusion relation. diffusion limit the

for

coeffioient Independent ooeffioient single

oonduotivity ooeffioient

DG

partiole (fig.

diffusion 2).

D*

SAMPLE 0 0

2

t x :

A

Na K Na K

6 5.9 106.5 60.9 9 0.6

G2 G3 G3

Na K K

205.0 74.0 95.5

lg [ I+(

OZl ED i-z

Ti”Cl

Gl Gl G2 G2

(In)".

cos(ffl)]

n: 0.65

0 I

I

I

I

I

I

2

1

0

1

2

3

-

Normalized 3.

FIGUIW 1 dependence

of

conductivity

DISCUSSION First

the

frequency

I 9 WT

bulk

note the diffusion

port than coeffioient at suffioient motion. From the ooeffiaient

with

< the

pic ions.

effeots Thus,

alkali of

different coeffioient

ion marked high

mew

of provided

motion is partiolee. ooncentrations

possible. Differences

D*

is

indioating

CTRV-model (eq. 2) the statio ia given by 2 0~4, t= t ti (t) dt 65 1 mean waiting time. Neglecting $ (t) should be all the differenoe

OG and D no other

the

*

DG represents

.

charge

the between oorrelated

limit

of

trans-

diffusion them

arise particle

the

diffusion

(5) the

same for both between DGand

influenoe bulk D*ia

of

isoto-

and traoer inolosed in,'.

-

Gl,Na

---

G1.K

1 lo3

diffusion shape

dence rather by the fy this glasses

8.

3)

Ch.

in

the the

chemical "universal"

G is connected with than with fluctuations

vitreous point with

REFERENCES 1) H. B6ttger (Akademie-Verlw 2)

of

by changes suppose that

of

Soher Kaps,

[K-l]

experiment it is evident hopping iona. Conductivity the frequenoy dependence

between

effeoted Thus we

T-’

FIGURE 2 of diffusion ooeffioienta curves of the glasses are omitted for clarity

Temperature dependenoe G 1. The oorresponding similar behaviour and From the interaotion that the

3

2

in the glass G 2 and G 3 show

that of

there is measurements conductivity

composition power law

interaotions of the

of the frequenoy

between

energy

struoture of the glass network. further investigations are necaesary lower alkali oonoentrations.

and and E.

V.V. Bryksin, Hopping Berlin, 1985). M.

Lax,

Kahnt

and

Phys.

Rev.

A.

Felt=,

B 7

Silikatteohnik

oarriers

introduced

However to especially

Conduction (1973)

glasses. depen-

ohzmge

potential

Borne show is not

in

Solids

36

(1985)

clarion

4491. 255.