Point defects of tephroite. I: The electrical conductivity of Mn2SiO4

für

197-218

Bd. 206, S.

1998

Zeitschrift

by

(1998)

Chemie,

Physikalische

R.

©

München

Oldenbourg Verlag,

Defects of

The Electrical

Point

I:

Tephroite.

Conductivity

of

Mn2Si04

Stiiber and

By

Christoph

Wolfgang Laqua

Giefien,

Institut für

Heinrich-Buff-Ring

und

58, D-35392

Chemie I,

Germany

Anorganische

Analytische

Justus-Liebig-Universitàt

GieBen,

Dedicated

to

the

Hermann

on

Schmalzried

conductivity

Professor

^occasionof^{his 65th}birthday

March

25, 1997)

(Received

Olivin

I

Electrical

of

I

(Mn2SiOJ

Point-defect equilibria

electrical

from the

The

melt,

of

conductivity

single crystalline Mn2Si04 (tephroite)

grown

was

between 1101 and 1197°C ^asfunction

spectroscopy

'6

by

investigated

impedance

^

within the

~10

0.21

is

(air). Mn2SiO„ n-conducting

activity

range

oxygen

within the

within the low and

high oxygen-activity regime, independent

p-conducting

are buffered

MnO or

we

whether the

MnSi03.

sample

against

a

model the

Based on our

results

the

point-defect

majority

experimental

propose

Mn,+-ions

in

sublattice

on Si-lattice

defects of which ^arevacancies

V"m„,

manganese

e'.

and electrons

wherein

associates

sites

holes h"

Mn'si,

(= Mn'M„)

(fayalite),

to

results of Naka-

model works without

Unlike

Fe,Si04

according

thermogravimetric

and

mura

our defect

in

Schmalzried

the

exist,

to exist

{Fe^Fei,}'

[1]

this con-

We drew

tephroite.

our

analogous species {Mn'MnMns,}'

postulating

is

which

followed

measured on

clusion from the

law

a-a02-plots

1/5.5-power

by

in the

whereas Nakamura and Schmalzried de-

stoichiometric

rived ^an1/5.0

high-a„, regime,

tephroite

from

in

the

range

of similar

activi-

law

their measurements

oxygen

power

likewise stoichiometric

ties on

The

fayalite.

constants for formation reactions of the aforementioned defects,

equilibrium

from our

were used to

which

describe the

experiments

depict Kröger-Vink diagrams; they

oxygen

emerged

of defect concentrations on

activities for both MnO

dependence

resp.

MnSiO, buffered

tephroite.

1. Introduction

otherwise known

the mineral

with

as

Mn2Si04,

tephro-

Manganese-orthosilicate,

members

Its

the

oxy-

the

to

ite,

crystallize

olivine-type family.

belongs

whereas the

in

ions

cations

an

hexagonal-close packed

approximately

array,

gen

of

coordinated sites with different

two

octahedrally

types

occupy

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Stüber and

198

Christoph

Wolfgang Laqua

_designatedMl

and M2 in the literature

olivine is member of the solid-solution series between forsterite

The rock

[2].

point-group

symmetry,

a

forming

Sometimes it contains

mi-

and

as

a

(Fe2Si04).

fayalite

component.

tephroite

(Mg2Si04)

nor

third

Olivine is

main constituent of the earth's

a

upper

for-

Because

mantle and determines

extend the mantle

form solid solution series without

to

a

large

rheology.

and

elevated

misci-

be

to

olivines

such

sterite,

fayalite

tephroite

any

rarely

end

at

are

members

the

pure

Besides

bility

gap

temperatures,

found in natural rock

assemblages.

naturally occurring

well known

and

of

there

are

examples

synthetically prepared compounds

an

olivine-type

electrical

which also have

structure.

as

Ni2Si04,

Co2Si04

and

such

as

diffusion,

conductivity

Transport properties

creep

their

behaviour of olivines

are

point-defect thermodynamics

governed by

essential for

of such

their

have

to

Hence it is

knowledge

an

[3, 4].

exact

understanding

properties

concentrations and

of the main kind of

defects,

point

variables.

from the

independent thermodynamic

dependencies

available then from the

theo-

and

Naka-

Based

on

results,

literature,

for forsterite

experimental

models have been

problem

retical

olivine

[5]

point-defect

developed

The

has been tackled

more

[6 8].

fundamentally by

of

who delt with

and Schmalzried

mura

[1],

thermodynamics

point-defect

results

on

to

synthetic fayalite.

fayalite

therrnogravimetric

of the

authors have been

used

com-

Ever

since,

conceptions

foregoing

widely

in

creep

minerals and

to

olivine-type

explain

phenomena

mass-transport

of

diffusion

We refer

to

[9, 10],

phenomena

pounds.

investigations

and

Numerous

of

in

15]

[11

potential gradients [16—18].

demixing

oxygen

known

the electrical conduc-

are

concerning

investigations

Reference is

here

to

[19—33].

given

only

tivity

olivine-type compounds

because

of the elder literature

less

not

some

more or

results,

recently published

quite unambiguous

the

not

due

the fact that

to

all

data

are

independent

fixed.

variables

were

thermodynamic

adequately

In

we

on

of

the electrical

this

paper

conductivity

synthetic tephro-

report

function

Our

MnO buffered and

buffered conditions

ite under both

as

MnSi03

and

of

(1097-1223°C)

(~10_I6-0.21).

activity

oxygen

temperature

results will be

the basis of Nakamura and Schmalzried's defect

on

analysed

for

This model is made

familiar

of three

of

model

defects,

[1].

fayalite

point

types

up

notation is used

two of them

we are

with,

namely (Kroger-Vink

and

cationic vacancies

holes h*

as

a

Fe'Fe). However,

V¡¡,„

(=

throughout)

result of these author's data

it

that third

out

most

came

a

analysis

striking

defect exists in

that is the associated

fayalite,

Fe3+-ion

species {Fe^FesJ*

majority

and

located

Si-lattice site

hole

a

an

on

a

Fepe

Fes,.

an

containing

whether

the existence of

not

anal-

Our discussion is focused

on

or

is consistent with

results.

associate

As will be shown

our

{Mn^MniJ'

experimental

ogous

defect model for

lacks such

our

an

later,

point

tephroite

associated

species.

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Point

I: The

199

Defects of

Electrical

of Mn2Si04

Conductivity

Tephroite.

Some

will be

who

under similar

room

[30],

to

of

results with those of

of

a

our

given

comparison

et

Bai

al.

the electrical

investigated

conductivity

tephroite

from

conditions

extended

as ours

single crystals

thermodynamic

apart

the fact that

have been

our

measurements

lower

activi-

to

oxygen

ties

IO16

IO10

in

in this

work,

[30]).

2

( 2

2.

techniques

preparation

Experimental

Sample

2.1

was

from

and sil-

Mn2Si04

Si02

MnC204,

(99.9%,

synthesized

manganese(II)oxalate,

icagel,

MnC204

The

(99.9%, Merck).

from metallic

was

Riedel

de

prepared

manganese

acetic acid. The solution

metal

solved in

was

diluted

was

Haën).

glacial

with the

colour)

amount of

same

water

3

MnC204

H20 (of

light

whereupon

pink

dilute

was

solution of ammonium oxalate

a

precipitated by adding

in

heated within 30 minutes

2

mol

was

ratio

under

to the

The

excess

(c

1.1:1)

l"1)

(molar

stirring.

suspension

formed

and

was

up

boiling point

room

afterwards

cooled down

this

of

to

within

6

hours

on

a

slowly

course

temperature

sand bath.

In

the

3

loses

H20,

MnC204

H20

procedure

trihydrated

one

mole of

colourless

to

2

water,

MnC204

oxalate

thereby transforming

which

filtered

washed and dried.

was

The

remove

be

must

off,

dihydrated

some

to

150°C

held

in air for

of

hours

at

the

The

was

water.

these conditions

remaining

under

the

reaction

completeness

decomposition

an

in

ran

extra

The Mn-content of

proved

by thermogravimetric

analysis.

the

oxalate

controlled

was

wet-chemical

by

analy-

as-prepared

manganese

was

sis. The

achieved.

dried

250°C in air

at

until

was

silicagel

weight

constancy

Then both the

were

educt

agate

and

MnC204

Si02

components

finely

ground

to

an

for

2

hours in

under

methanol in

mortar

proportions according

the formula

with

on

2.00

(Mn,Si)3-3lS04

1.774;

(stoichio-

n(MnO)/n(Si02)

and 2.061. Based

the results of Sandner

and

the ratio

way

metric)

[34]

Laqua

of the mole

a

numbers of MnO and

chosen

at one

was

in such

the

that

Si02

saturation of the

lattice with MnO

side of

small homo-

established

Mn2Si04

was

and with

at the other side

MnSi03

geneity

range

below).

definitely

(see

After

mixture

of the methanol and

the

evaporation

subsequent drying,

into small

powder

diameter,

was

mm

hydrostatically pressed

pellets (10

within stainless-steel

matrice and

prere-

1.5

15

mm

a

kbar)

high;

pressure

a

acted

600°C for

4

were

and

1100°C for

6

in

h

at

h

at

atmos-

CO/C02

(10:90)

The

and heated

where

1400°C for

at

2 h

phere.

pellets

ground again

( 2

in

5

formed

a

trans-

Pt-crucible,

IO"11)

finger-like

they

nearly

melt.

parent

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Stüber and

200

After all the

Christoph

Wolfgang Laqua

the

bubbles within the melt had

crystalli-

gas

disappeared,

the crucible down the

zation

initiated

was

vertically operating

by pulling

2

At

1200°C the crucible movement

of mm/h.

SiC-tube furnace

at

for

Pt

a

speed

the

let

to

hours

solidified melt

8

in order

was

mechanically

interrupted

the

After

room

crucible had reached

relax.

could

formed

the

be

platinum

temperature

had been

which

such

detached from the

tephroite oligocrystal,

easily

On

process.

the

oligocrystals

crystallization

average

overall

an

during

volume of

within

contained 5—7 smaller

cm3

crystal

single crystals

96-98% of the theo-

reached

of the

about

1

(the

oligocrystals

density

retical

value).

Samples

<

found

2)

composition

be dark

to

were

>

with

ones

an

(n(Mn)/n(Si)

2)

Si02-excess

an

of

(n(Mn)/

were

with

MnO-excess

the

(n(Mn)/n(Si)

stoichiometric

a

light-

greyish,

with

whereas

colour,

2)

samples

green

«(Si)

It

brownish.

be

by

to

appeared

and

small

mi-

of

established

was

optical

electron-microprobe analysis

that

contained

amounts

with

Si02-excess

samples

croscopy

MnSi03,

with

a

of

contained small amounts

whereas

Si02-deficit

samples

that both the

second

which

MnO

as

thermodynamic

compo-

proved

phase,

fixed.

and

activities

were

nent

aMnsio,

aM„0

definitely

measurements

2.2 Electrical

For

conductivity

electrical

used

ana-

of the

we

an

measurements

impedance

conductivity

which

from

in the

model

4192A),

(Hewlett-Packard,

operates

range

lyzer

into small bars with

cut

in

a

The

MHz.

were

5

Hz to

1

tephroite

to

oligocrystals

4—7

mm

in

small rods

and

mm

saw

diamond

diameter,

(7

ground

with dia-

then

surfaces of

wheel. The

size

diamond

a

achieved

samples

was

The

polishing

0.25

to

minutes. Both

using

length) by

down

some

were

of different

mond

paste

pm.

grain

water

were

in

for

cleaned

opposite

ultrasonically

with

from 50

Afterwards

thick

two

the

num

platinum.

plati-

sputtered

cut

cylindrical sample

sheet

a

electrodes

pm

platinum

(Mn-presaturated),

coated surfaces and

these

to

were

held

attached

together by spring

platinum

loading.

We

in the lower

ac-

with

fixed the

CO/C02-mixtures

activity

oxygen

mixtures

1101

was

wait until

<

with Ar

Ti

IO

and

over

sponge)/02

4)

range

(purified

tivity

( 2

range

upper

^

the

in the

( 0,

10~4);

activity

temperature range

we

chemical

The time

had

the

1197°C.

of

were

to

All

to

grade.

gases

state

been reached after

has

a

new

changing

equilibrium

gas compo-

low activities. All

activities. We

activities and

8

h

at

varied between

2

h

sition

at

high

from lower

from

to

measurements were

higher

performed

oxygen

lower activities because it

to

did

took

measurements

not

to

higher

perform

a

new

The

was

in

low

gas

reach

to

time

after

altered in

the

a

activity regime

long

especially

3

state

(—2

composition

days).

state

changing

equilibrium

temperature

10°C

each

new

was

equilibrium

steps;

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Point

I: The

Electrical

201

Defects

2

of

Mn:Si04

Tephroite.

3

Conductivity

4

3

1

1. Sketch

of the

to

Glas

for the electrical

Fig.

on

measurements

experimental

equipment

conductivity

analyser.

BNC connections

to

Aluminum

2)

(not

scale). 1)

flange. 4)

tephroite

impedance

front sheet.

Socket

for

the

connections.

3)

head.

corundum

thermocouple

5)

Measuring

Seven-hole

corundum rod,

Pt/Pt-10%-Rh

6)

Inner

thermocouple. 7)

bearing

tube with

sew-out slit

access.

Outer

8)

corundum

tube

allowing

sample

protecting

(one-

side closed).

Adjustable

Corundum sheets

and corundum block

Gas outlet.

9)

(sample holder). 10)

Sample. 11)

stainless steel

Gas

seal.

inlet.

12)

13)

O-ring

14)

springs.

reached after

and

runs.

about 20 minutes.

Measurements

were

be

with

both such

performed

rising

No differences

could

detected for

temperatures.

falling

activities

were controlled with

a

solid-state

outside the

cell

Oxygen

(CaO-

galvanic

stabilized

an extra

The

sensor

installed

was

zirconia).

cell in

measur-

impedance

in

the

of

cover as

furnace

the immediate

placed

vicinity

impedance

device

to

the distance

the

feasible

has

to

as

to

short

and

ing

keep

gas

possible.

With

a

valve it

oxygen

was

three-path

consecutively

alternatively

the

the inlet

at

and the outlet of the

leaks in

cell

monitoring

activity

equip-

thus

aware

corundum

made

were

of

the

tubes

ment,

immediately

becoming

oxygen

tube that surrounded the

cell. All

impedance

leading

gas

of

The

of

the

which connected

the

tubes,

single

copper.

of the

parts

copper

compo-

nents

two

(two

Germany,

containers,

gas-supply

system

gas

high

accuracy

gas-

meas-

reliance

the

Woesthoff,

±1%),

mixing

pumps,

impedance

cell

minimize

and the

device

cold welded via

were

to

uring

a02-monitoring

fittings

leaks

sketch

of

the connections

far

at

as

gas

possible.

A

scale).

our

is

shown in

1

impedance measuring

(not

assembly

Fig.

so

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Stüber and

202

Christoph

Wolfgang Laqua

Ccell

z'

/kn

of

fixed

Hz-1

and calculated

lines)

2.

spectra (5

MHz)

(full

Fig.

Experimental

impedance

1191°C. The MnO

is

different

activities at

for

activity

tephroite

oxygen

circuit is

Havriliak-Negami element).

synthetic

cell

^asinsert

1. The

at

bulk

(C„K

capacitance, RB

depicted

equivalent

aM„0

ZHN

resistivity,

with

SiC

tube furnace

a

The

element. The

was

equipped

heating

high-temperature

a

was

with

820,

PID-regulator (Type

adjusted

temperature

An

furnace

a

was

interface

The

used

to

RS 232

temperature.

with resolution

Eurotherm,

regulate

temperature

at

computer

Germany).

index value of the

of

and control the

1

be

of °C. The fluctuation

could

temperature

given

than

was

index

measured

±0.2°C. The thermo-emf

value

less

the

50°C-cold

a

junction.

against

with the

The

recorded

were

analysed

programme

the authors

impedance spectra

which is

version,

in the

actualized

the

LEVM

[36]

[35]

continuously

In

by

on

feature

two

which is available

and

general,

spectra

request.

in

2.

the

is

an

However,

semicircles;

semicircle

high-frequency

Fig.

example

given

IO"11 in

of

2. To make the full

9.7 10

be

1

case

seen at

can

2

Fig.

only

·

in

of

has

to

semicircle visible

one

to

",

a0,

1.0 10

low-frequency

7

the scale has

be

in

reduce the

whereas

case

scale,

a0l

varied cell dimensions

with

one

not

were

Investigations

systematically

enlarged.

the cell

section. It

in

of

runs we

our

However,

considerably changed

performed.

the values described in the

dimensions

to

foregoing

not

compared

has

electrical

turned

further

of _an

that the

out

altered,

conductivity

giving

specific

on

of the

data

the basis

to

our

experimental

interpretation

support

which is outlined below.

circuit

equivalent

bulk

the

where-

attribute the

semicircle

We

to

low-frequency

conditions of

resistance,

high-frequency

as

semicircle. The

interface resistance is mirrored

the

interface

by

and

estimated under

resistance,

decreasing

increasing

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of

Point Defects of

I

:

The

203

Electrical

Mn2Si04

Conductivity

Tephroite.

a

inter-

shows distinct

which is

an

to

hysteresis,

helpful

temperature

separate

face and bulk

Beside that

of

interface resistance which

part

properties.

is

with

located

second

formed

the

at

we

to

have

deal

thick rhodonite

usually

electrode/sample phase boundary

a

some

pm

interface

electrode material.

which

from thin

originates

part,

the

electrode

the

at

fact

layer,

tephroite-platinum

despite

were

that

foils

the

used

as

Mn-presaturated platinum

As

can

seen

be

from

interface

resistance increases

the Mn formed

2,

Fig.

drastically

with

the reaction

activities.

to

oxygen

decreasing

Apparently,

according

Mn

+

1/2

Mn2Si04

diffuses

MnSiO,

02

the

foil

the alumina

to

through

Mn-presaturated platinum

support

reacts

the

at

outer electrode interface where it

this

spinel

manganese

influenced

the

be

seems to

ac-

MnAl204;

strongly

process

by

oxygen

To make

the

that the

still

sure

remained in the buffered

that thin

tivity.

tephroite samples

state

measurements

the fact

rhodonite

tephroite

during

impedance

despite

are

we

formed

the electrode

at

each

interface,

layers

investigated

run

after

with the electron

were

an

In all

cases,

sample

experimental

microprobe.

of

traces

MnO

buffer

of the low

detectable

within the

MnSi03

resp.

tephroite

matrix.

the

From the

semicircle

conclude that

we

shape

frequency

of the

carriers

the rhodonite

the

interface

of

movement

elec-

MnSi03/Pt(Mn)

permeation

charge

through

is diffusion controlled. Within

the

layer

carriers in the

Mn2+-ions

tronic

electrical field is

charge

alternating

the

in

superimposed by

a

diffusion of

chemical

which is

estab-

activity gradient,

an

leads

turn to

be described

lished

unknown within the rhodonite

of the relaxation

even

This in

can

layer.

which

times,

asymmetrical dispersion

by

use

of the

element

The overall

[35].

circuit,

empirical Havriliak-Negami

impedance

then be

insert in

can

an

as an

analysed by

equivalent

spectra

Fig.

given

has been achieved

2. The estimation of the

single

components

by

nonlinear

least

As

can

[36]).

agree

CNLS-regression (complex

squares regression

be

from

the

and calculated

seen

excel-

2,

Fig.

experimental

spectra

lently.

3. Point defect

of

tephroite

thermodynamics

3.1

in

with

MnO

MnSi03

field)

Tephroite

into

equilibrium

(two-phase

resp.

e'

the defects

our

and

account

as

Mn'Mn,

VI,

MnSi

Taking

majority point

of

defects in accordance with

results

the

on

non-stoichiometry

tephroite

able

write down the

to

defect reactions:

we are

[34],

following

+

2

+

1/2

3

02

MnSi03

+

Mn¿n

·

Mn2Si04

V£n

(1)

+

3

1/2

2

Mn¿„

Sis*

Mn2Si04

Mns,

MnSi03.

·

(2)

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204

Stüber

and

Christoph

Wolfgang

Laqua

the mass-action

concentrations

The

dence of

ables

of

defect

1

law leads

for the

to

application

expressions

depen-

vari-

the

on

independent thermodynamic

in

case):

any

(aM„2Si0i

(3)

(4)

[ · ]2[ ]

[MnUtMnL]

<

KiaMnSt0,

K2

aMiSÌO,

fraction of

defects

their

the site

the

sublattice

on

tephroite).

the concentration of

[ ]

designates

respective

for

1

stoichiometric

([ µ ] [Sisi]

The concentration of electrons

on

Mn'Mn

(5)

depends

the intrinsic defect

defects

to

according

equilibrium

.

[Mn-Mn][e']

The

condition reads

electroneutrality

[VSJ [May

+

2

4

2

(6)

[e']

[Mn^J.

that the electrons

located

the cationic sublattice _;

are

in

and

It has been assumed

this the factor

2

in front of

in the

above

[Mn"Mn]

[e'], [V'm„]

we can

explains

equation.

With

of

the hole concentrations

the

of the

(3) —(6)

help

Eqs.

express

function

variables

and

as

űMnsio,:

a0:

independent thermodynamic

1

·

⁺y^K2

2

+

Kt

^[MnJ.

aMnSi0,

aMlsi0i

[ · ]3

a£

^ ^]

(7)

and

well.

as

^for[Vl]

be derived

can

[MnsJ

Analogous expressions

been

from

seen

which describes the

of the

As

can

(7),

Eq.

dependence

the

hole concentration

on

Mn2Si04/

as soon

oxygen

activity along

phase boundary

will be

numerical calculations

with

values

1>

MnSi03

ÛMnsiOi

possible

for the mass-action law

are

and

constants

in

available.

as

Kt, K2

Kei

These

calculations will be

4.3.

performed

chapter

If

from

saturated with

we

to

ac-

we

MnSi03

(ümhs¡oí

1)

tephroite

change

MnO-saturated

in

have

calculate the rhodonite

to

1),

(aMn0

samples

in

with MnO in

order

to

use

(7)

tivity tephroite equilibrium

correctly

Eq.

that

in

case.

AG°

Values of the standard Gibbs

for the

formation

tephroite

energy

MnO

reaction from rhodonite and

to

according

+

MnO

Mn2Si04

MnSi03

(8)

known from the literature

are

cedure

a

[34, 37, 38].

pro-

least-squares fitting

By

received the

we

relationship

'

+

7mol

(9)

AG%

14^

^-38,300

our

which

used in

calculations.

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Point Defects of

I

:

The

205

Electrical

of Mn2Si04

Conductivity

Tephroite.

field

3.2

within the

Tephroite

one-phase

In

derive

within the

between the

to

a

order

relation

hole concentration and

oxygen

field

first

coincides

combine the chemical reaction

(which

activity

tephroite one-phase

approximately

with

we

stoichiometric

and

composition),

this

(1)

(2)

+

MnSi03;

by eliminating

Sis*

Eqs.

10

yields:

+

7

2

Mn*n

02

Mn2Si04

(10)

Mns,

Mn^n.

3V1

The mass-action law for

reads

(10)

Eq.

[MnM„]7[V^n]3[Mn:si]

(11)

= \ 2 2 2.

The mass-action law for

the

electronic defect

which

(intrinsic)

equilibrium,

is

valid

of

is

as

indepenent

Ktì

solve for the four defect

activity given

oxygen

[MnJ[e']

(12)

To

we

concentrations

One of these is the

and

condition

[Mn^J,

[MnSi]

[Vi],

[e']

need

two

more

equations.

electroneutrality

2

+

2

4

[Mm]

[MnSi]

(13)

from which

[e']

be

[V£j

one we are

The other

the

for

can

taken from

(10),

looking

Eq.

relation

in

between the concentration of defects

is

that

and

[Vl]

following

:

case

stoichiometric in

[MnsJ

emerges

tephroite

composition

[Mi&]

[VI]

(14)

Because

of the

electronic defect

validity

(intrinsic)

equilibrium

be deduced

other

relations between defect concentrations

no

can

(12),

Eq.

from

for

arrive

we

at

(11)-(14)

[ · „],

(10). Solving

Eq.

Eqs.

/

\

1/4

g

+

[MnU3

(15)

—[

(K\ K2y'W£[Mn-M„YM

that is

KJMnU

J

We

the whole

within

have

to

(15)

oxygen

emphasize

Eq.

appliceable

experiments.

hole concentration

in

covered

we

our

activity

range

the

on

oxygen

we

Concerning

dependence

activity

within the

field

concentration

small,

at

back

to

activities,

only high

go

tephroite one-phase

Because the

as

of

electrons

at

activities is

(13).

Eq.

high

oxygen

condition

be considered

the

to

(13)

neglegible

electroneutrality

Eq.

reduces to

+

2

4

.

[MnJJ

into

[Mnsi]

we

[VI]

(16)

con-

second

account

relation between the

that is

a

Taking

(14),

yield

tephroite one-phase

Eq.

centration of defects within the

field,

.

[ · ]

[VI]

(17)

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206

Stüber and

Christoph

Wolfgang

Laqua

can

This

also

be derived from

within the

designated

(10)

relationship

directly

the

linked

high-

Eq.

that mole

as

fact,

by

fractions,

( )

region remembering

oxygen

factor of

and site fractions

2

for Mn-lattice sites in

are

a

[

]

2

for instance.

and

into

(14)

(Mn^J

[Mn^J

(17)

tephroite,

Inserting

Eqs.

arrive

at

we

(11)

Eq.

-

(18)

[ · ]

K2)"u <55

(yjYyjV?

seen

as

As

be

from

function of the

the hole concentration has

1/5.5-

model is

concen-

to

an

can

(18)

Eq.

obey

in

that

law

case

our

for the

vacancy

activity

power

oxygen

the

is

true

correct.

to

same

(17)

According

Eq.

we

law which

derived from

tration

our

It

this

was

[Vm„].

1/5.5-power

exactly

of the

of

measurements

function of

as

(Mn,Si)3_3<504

tephroite

nonstoichiometry

a

[34].

activity

oxygen

point

we

no

this

have

that

defect associates

in

At

to

emphasize

appear

associates,

so

to

defect model

far in

contrast

our

developed

{Fe^FesJ*

role in the model

Nakamura and

which

Schmalzried for

an

play

important

depicted by

seems

it

reasonable

to

[1].

fayalite

Consequently,

quite

described in this

defects.

the

results

majority

tentatively interprete

conductivity

by only

paper

e'

and

as

Mn"Mn,

Mn5i

V^,

utilizing

4. Data

analysis

of

conductivities from

conductivities

4.1

overall

Separation

partial

The electrical

of the

partial

conductor is

of

electrons and holes

of _anelectronic

the

as

sum

(19)

given

conductivity

and

conductivities

„

ah

+

oh.

In

our case

the concentration of holes is identical with the concentration of

leads

to

the

which

the

for the

MnMn-defect

species,

following expression

total electrical

conductivity

+

Mh[Mn-Mn])

(20)

-y- ^(Me[e']

F

cal

u

molar volume of

electrochemi-

constant, Vm

Faraday's

mobility.

tephroite,

the abbreviation

Using

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of

I: The

207

Electrical

of

Mn2Si04

Point Defects

Conductivity

Tephroite.

reads

fs[e']

(20)

Eq.

+

(22)

can

fh[Mn-Mn]

section it will be

In the

be

how the hole

shown,

ah

following

conductivity

from the

that

minimum

case

a

total

in

passes

separated

conductivity

in

on

the

is

dependence

activity.

oxygen

multiplied through by

the

First,

(see

(21));

Eq.

(12)

Eq.

product/e/h

one

gets

K°.

ac-ah

(23)

*„, /.·/„

into

Insertion

(19)

Eq.

yields

+

jK^iA,

CT

(7h

(24)

is valid

Because

without

any

it

are

hold for the

must

con-

restrictions,

values

(23)

Eq.

minimum

that is

marked

itself,

an

(minimum

ductivity

zero

by

upper

index)

a°c al

(25)

Kelfefh.

the minimum of

At

both

conductivities

thus

have

are

we

;

partial

equal

a0

al

cfl

(26)

we

this into

find

(21),

Introducing

Eq.

(27)

Kclfcfì.

In strict

zero'th order

this

a

is valid

we assume

.

the minimum

sense,

at

of

uh

In

a

expression

only

that the hole

on

and the

Based

approximation

mobility

as

are

mobilit

of electrons

well

uc

oxygen

independent

activity.

this

on

alters into

(27)

assumption Eq.

(28)

=Kelfefb.

)

the last

with

have

we

(24),

Combining

expression

Eq.

finally

-

„

(29)

The

hole conductivities

from

overall

to

conductivities

„

possibility

to

separate

will

facilitate

enormously

equilibrium

the mathematical

Eqs. (3)-(5)

(29)

according

Eq.

pro-

cedure in

values for the

constants

will

as

getting

be shown in section

4.3.

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Stüber and

208

Christoph

Wolfgang

Laqua

and

concentrations

on

4.2 Electrical

conductivity

point-defect

of hole conductivities

is

activities

for the

be obtained from

(MnSiO,

one-phase region,

Expressions

dependence

Eq.

oxygen

can

valid for the

which

(7),

two-phase region

easily

or

and from

of

MnO

(15)

at

(18)

saturation)

resp.

tephroite

Eq.

valid

where the latter is

for the

oxygen

only

high

basis of the

the

on

activities,

following equation

F

(30)

Mh[Mn-Mn]

„

'm

well.

is inherent in

as

(20)

(30)

Eq.

The

reads

for the

(7)):

Eq.

(see

two-phase region

expression

1

1/2

ß~ 2

·

+

2

(31)

(see

|

<

0~h-

aM"Si0'

0~l

ŰMnSiO,

~2~

have the

abbreviations used in

The

Eq.

(31)

following meaning

Eq.

(21))

(32)

(33)

(34)

K,

Kt-fh

K2-fh

Ka-fl.

K2

Kd

We

within the

and

field exclusive-

which is valid

via

to

arrive at an

field

(31),

Eq.

expression analogous

whole

the

over

(30),

(15)

Eqs.

oxygen

expression

activity

one-phase

range

at

here. The

for the

which is not

one-phase

given

is:

activities

(18))

Eq.

(see

oxygen

high

ly

(35)

„

R^ni<5·

(yj

)

Mathematical

4.3

procedure

°

and

from

estimate values for

In order to

our

,

Ks,

K„

experimental

calculate

data and

be able

to

f(a02) plots,

=/( 2)

subsequently

follows.

as

we

proceeded

solve this

for

would have been

The

to

most

straightforward

problem

way

for

and the

insert

one

to

for

(31)

(19)

instance)

<rh

analogous

expressions

(Eq.

into

and

find the above mentioned

However,

to

here)

(not

cre

trying

appropriate fitting procedure.

handle mathematics

given

Eq.

was

because it

we

an

by

parameters

hard

have choosen

task

the

too

a

to

bulky

properly

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Point

I _:

The

209

Defects of

Electrical

of

Mn,Si04

Tephroite.

Conductivity

another

in

of

only

reliable values for

involved

er°

and

Kci

partial

via

a

Ku

finding

method,

way

is

instead

of both

which

the

conductivities

ah

„

and

<rc.

values for

the minima

values of

from

First,

°,

the

overall conductivities

deduced

were

data. These

first

by spline

interpolation

experimental

values

which

will

for

themselves

then be included

separate

er°,

in the

values from the

pro-

ac-

fitting

cedure described

were

used

to

below,

ct's

o~h

to

(29).

cording

Eq.

we

a

transformation

of

Afterwards,

variables with

which

of the

from

performed

„,

a

enabled

constants

via

us

find

to

first

set

a

weighted

polynomial

regression

and

linear

The

calculation of

Ku K2

Kcl

by

ah

regression.

then be

out

an

could

carried

iteration

(31)

Eq.

from

the

roots

procedure

by

of

(31).

Eq.

The

non-linear

a

of

the

values

for

step

regression

experimental

we are

the GauB-Newton

to

Because

an

according

procedure.

looking

matrix

solution of

the non-linear

in order

solve the deviation

to

(31)

explicit

Eq.

(Jacobi

is

matrix),

not

regression procedure

directly

applicable.

Therefore

forced in

we were

a

to solve

and

and all

preceding

step

Eqs. (29)

(31)

simultaneous minimization.

the other mathematical

This

values for

numerically

by

way,

such

as soon as

for

(deviations

as

instance)

parameters

,/

calculable

in consecutive iterations

available.

were

this

for

set

K„

starting

and

was

K2

Kcl

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Stiiber and

210

Christoph

Wolfgang Laqua

aiMnO"1

O

°C

T=1197

T=1155 °C

T=1101 °C

A-,-1-,-1-,-1-,-I-!-1-1-1-1-1-1-1-1-1-.-1

-8

0

-12

-4

-16

of

as

a

function of the

4.

electrical

and 1155°C. The

activity

Fig.

at

are

conductivity

tephroite

oxygen

Specific

MnO

is fixed at

MnO/Mn,Oj-phase boundary

1. Calculated values

1197, 1101,

aMn0

activity

indicated

is

full

The

as

lines

5).

(see chapter

given

by

a

broken line.

5. Results

i.e.

we

in

For all

our

on

(Mn,Si)3_3¿04,

composition

samples

independent

electrical

found minimum for the

a

(overall

examples

conductivity

conductivity)

for these

Characteristic

on

depen-

dependence

activity.

oxygen

in

dencies

are

3

5.

Figs.

given

well-defined in

with silicon

in both the other

The minima

excess

cases

are

samples

less

are

1);

they

pronounced

(a(MnSi03)

2, stoichiometric).

1;

(a(MnO)

«(Mn)/n(Si)

conclude

the existence of the minima

that

whereas the

conduction

become

From

we

>

p-type

activities

oxygen

at

samples

high

( 2

2)

prevails

oxygen

<

activities

lower

at

£,).

conducting

( 2

-type

excellent

is obtained between

In all

cases an

curves

experimental

agreement

calculated

and

1155°C and

outlined in the

section.

and

as

foregoing

points

our

which

from

Values for

are

Ku K2

Kel,

emerged

in

fitting procedure

1.

Included in Table

1

1197°C

listed for

Table

some

for

below. The

in Table

and

which will be of

in the discussion

the basis of

data,

values

K2

K°,

K\

importance

on

values calculated

between

given

agreement

and

is excellent

values

1

3-5).

(Figs.

experimental

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of

Point

I The

:

211

Defects

Electrical

2

of Mn,Si04

Conductivity

Tephroite.

n(Mn)

n(Si)

=

-2.0

-3.CH

-4.0

cu)

o

°c

t=1197

t=1155

t=1101

16

-ta

5.

electrical

and 1155°C. The

2).

of

function

of the

stoichiometric in

as

a

Fig.

at

Specific

conductivity

tephroite

activity

oxygen

are

1197,

(n(Mn)/n(Si)

1101,

tephroite

composition

samples

Table 1.

specific

Mass-action-law constants calculated from

the

values of the

experimental

electrical

of

tephroite

chapter 4.3).

(see

conductivity

1

"m,o

"( )

(Si)

aM,,s¡03

2

1197°C

-5.64±0.21

-4.15+0.07

-21.06±0.70

-8.04±0.29

-7.44±0.05

-6.02±0.05*

-7.85±0.04

lg£,

-4.22±0.06

-27.77±0.18

-9.20+0.04

-8.55±0.02

igK2

-22.26±0.09

-7.70±0.07

-7.21+0.02

\gKÌK2

lg£el

igK°

1155°C

-5.93±0.21

-4.29+0.07

-22.09±0.70

-8.09+0.29

-7.81+0.04

-6.29±0.05*

-8.07±0.02

-4.45±0.04

-28.67±0.11

-9.64±0.05

lgtf,

lgi?2

K2

-23.24±0.08

-7.97±0.09

-7.61 ±0.02

lg/c;

lg£e,

-9.01

±0.01

lg^°

*

Calculated

with

a

mean value of

K2.

6.

Discussion

As

that

be

from

defect

Vm„, µ„, Mnsi

model is based

e'

can

seen

our

the

on

3,

chapter

assumption

in

the four

and

of

are

only

species

importance

any

the defect

of

structure

depicting

tephroite.

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Stüber

212

and

Wolfgang

Christoph

Laqua

in

defects

(n(Mn)/

for different

Table 2. Values for the

majority

row

(lAi)log

exponent

log

with the

2

in the

indicated

in

which is

means

equilibrium

phases

tephroite

upper

2

n(Si))

"stoichiometric").

MnO

MnSiO,

Mn

Mn,04

n(Mn)

«(Si)

1/6

1/4

1/6

0

1

1/6

1/4

1/6

1/4.5

0

VI

·

1/5.5

;„ · „

1/5.0

and

1/4.5

0

{ ;, · }«

we

the

between

experiment

theory

good

Supported by

our

agreement

model

which allows for defect

conclude that

VI,

species

point-defect

e'

Defect

which

be

may

and

has realistic

a

associates,

Mnsi

Mn'Mn,

meaning.

the defect reaction

to

formed

according

+

(36)

·

{Mn^Mn^}'

Mn's,

our

exist

defect associates would

the

included in

in

model. If such

to

are not

in

actually

-

of

the

[1],

slope

log

fayalite {FepeFeSi}J

tephroite

analogy

be 1/5.0 for stoichiometric

had

of

to

(n(Mn)/ra(Si)

2)

2

tephroite

log

plots

whereas

case

we

an

found

in the

law in

1/5.5-power

activities,

In

range

oxygen

accordance with

high

of MnO-

(35).

MnSi03-saturated

if associ-

resp.

Eq.

we

of from

2) _;however,

would

an

2

we

1/6-power dependence

samples

expect

defect

Table

not

as

a

could

ates were

(see

majority

present

in

our

this value

verify

Having

experiments.

that

on

we

defect

taken into

account

have

in mind

not

species

have

we

an

as

sites such

to

interstitial

or

Sir"

Mn;'

give

explanation why

from

model. First of all it is well

defects have been ruled

these

out

our

in

on

via

cation diffusion

silicates

va-

regard-

conclusions about

established that

cancies. That

proceeds

olivine-type

Mn2+-cations

interstitial sites

best be

can at

means

it is

draw

ed

but

to

not

as

defects;

possible

measurements. As

minority

any

will be

from

defects from

our

seen

conductivity

minority

results from coulometric titration

can

a

[34]

experiments

forthcoming

paper

of interstitial

the existence

be

without

In

interpreted

postulating

consistently

a

Mn2+-ions

defect.

addition it follows from the literature

Mn2+ interstitials

as

majority

in MnO

that

even

[37]

are

investigated by thermogravimetry,

of

no

importance.

advanced

Si4+

interstitial

po-

Similar

In

can

on

concerning

arguments

consider

most

sitions.

accordance with Nakamura and Schmalzried

we

[1]

as

Si4+-interstitials

from

chemical

the

mere

a

energetically

viewpoint

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Point Defects of

The Electrical

of

Mn2Si04

I:

213

Tephroite.

Conductivity

to

unfavourable defect

in olivine. Moreover it is not

estab-

taking

species

possible

of

or

lish

an

(35))

[Vm„]

[Mn*Mn] (see

1/5.5-power dependence

Eq.

into

Si"" in addition

to

and

defect.

account

as a

V„„

Mn'Mn

majority

K°

and 1197°C

listed

Values for

and

1155

at

are

1,

2, el)

K, (i

in Table

1.

Whereas

is

of

decreases

The de-

as

K2

Kt

independent

composition

expected,

of

with

crease can

MnO content

about two orders

magnitude.

decreasing

by

that

MnO

in

be

an

excess

explained only by assuming

tephroite

hand raises the values for

the other

enhances the hole

to

which

on

K¡

mobility

(32).

according

Eq.

the hole

does

de-

also

We have

other evidence that

some

mobility

actually

for

the MnO concentration of

values

on

Ke¡

Obviously

pend

tephroite.

MnO

content

observe

much

3—5)

is the

increase with

with

not as

as

case

although

increasing

we

°

means

shift

of the

That

values

that

con-

a

Furthermore,

K¡.

(see

Figs.

lower

with

MnO

to

content.

potentials

increasing

oxygen

the

of holes

MnO

the

to

at

contents

according

higher mobility

higher

curves

dition for the minimum in the In

/(In 2)

ce

resp.

„

(37)

(38)

[ µ„]

we [e']

already

uh

realized

lower

is

at

Mn'Mn-concentrations.

the

hole

In order

obtain values for

mobilities from

constants

estimations of

to

we

our

Kt

and

from

have

refer

the

to

and

derived

obtained

104 cm2/

to

K¡

K2,

K2

equilibrium

coulometric titration

-7.120 and

1197°C

At

our

we

[34].

experiments

-4.182. This leads

4.8

to

K,

resp.

The

K2

log

^uhcnvYVs.

log

·

10~4

the

value is 5.3 10~4

Vs

5.8

mean

cnrTVs;

of the

constants

found

we

be inde-

was

to

K2

K\

equilibrium

product

authors cited

attrib-

of

the

above. Hence

have to

pendent

the

temperature by

of

estimated from

ute

measurements

our

K\

K2

dependence

temperature

conductivity

Table

the

to

of the hole

mo-

be

1)

(see

dependence

temperature

itself which is inherent in the

it

must

K\

K2.

product

Consequently

bility

deduce

of the

hole

the

K]

from

to

dependence

possible

temperature

mobility

versus

K2

of

l/T

is

the estimated value for

Arrhenius

an

6);

(see

£Ah

plot

Fig.

0.85

the activation

from this

our

eV.

the hole

plot

energy

3

results

of

In Table

we

concerning

mobility

olivines

and their relevant

teph-

compare

of

roite with the hole mobilities

oxides. Most

other

binary

is the fact that the

in the series

low value

striking

extremely

component

for the hole

of

Co2Si04, Fe2Si04, Mn2Si04

mobility

tephroite

reflect

low value for the hole

in MnO in the series

the

seems to

mobility

a

MnO. Our results for

and

mech-

CoO, FeO,

Eh

clearly

uh

hopping

of

suggest

for the electronic

anism

(small

mechanism)

polaron

conductivity

tephro-

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214

Stüber

and

Christoph

Wolfgang

Laqua

-22

-25

"I-1-1-1-1-1-1-1-1-1-1-1-1-1-1

0.74

0.67

0.69

0.68

0.70

0.72

0.71

0.73

1000

/

6.

the

mobility

of the

mass-action

temperature dependence

K'

of the

constants

The

Fig.

of

Temperature dependence

product

K2.

charge

slope

line is determined

the

carrier

straight

by

(see text).

3.

Table

of hole

metals.

for

mobilities

some

oxides

and

silicates of

ternary

Comparison

binary

°C

some 3d-transition

Réf.

«„

Compound

1

cm2V-'s

7

10-2

1100

1150

1200

Co2Si04

Fe,Si04

Mn2Si04

[21]

6-10-3

6

[22]

this

4

10

work

CoO

FeO

MnO

0.3

0.2

3

1150

1200

1150

|21]

[22]

[38]

2

10

ite.

the values for

and

estimate value for

we

the

a

Kel

Combining

uh

Kcl,

for

-8.43

value for

constant

the

electronic

(intrinsic)

(see

equilibrium

Eq. (12));

this

1197°C.

and

at

yields log Kei

of

use

our

with

the values for

the concentration

and

Kel

AT,

By

K2

of the defect

with the

along

taken from

able

and

calculate

function of

Eqs. (3)-(6)

we are

to

[34]

Vm„, MnSi, Mn„n

e' ^as

the

for

species

activity

oxygen

the

of

Eqs.

derived from

for the

field

and

help

expressions

two-phase

from

field.

(11)—(14)

one-phase

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I: The Electrical

of

Mn2Si04

Point Defects of

215

Tephroite.

Conductivity

7b.

for

1197°C

to

at

calculated for fixed

MnSiO,

ac-

Kröger-Vink

Fig.

diagram

tephroite

The broken lines

Mn,04/MnSi01/Mn2Si04

=1)·

Mn/MnSiOV

tivity

Mn2Si⁽0^a4^M„(^sl^¡e^o3ft)

correspond

three-phase

equilibria

resp.

(right).

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Stüber and

216

Christoph

Wolfgang Laqua

c

b

Bai

this

al

et

aMn0=l

aMnSi0s=l

study

n(Mn)/n(Si)=2

aMn0=l

-2H

O

aMnSi0s=l

-2

2

-18

14

-10

lg

-ß

ao2

of electrical

the

[30].

of

8.

of the

with literature data

conductivity

dependence

Comparison

Fig.

oxygen-activity

to

according

tephroite (this work)

at

1197°C for both the

on

The calculation has been carried

out

tephro-

7a)

or

MnO

the

hand

ite

in

with

in

one

Mn304

Mn,

(Fig.

phase

equilibrium

with

the other

and the

hand.

As

on

MnSiO,

7b)

equilibrium

(Fig.

tephroite phase

be

from

exists with

a

excess

can

seen

7a,

Fig.

the

tephroite

manganese

2

The

>

[Vi]) ^all

over

([Mns¡]

two-phase equilibrium tephroite/MnO.

2

[Vl]) ^is

very

with

stoichiometric

at

([MnSi]

10~20)

approached only

composition

where

in

is

activities

manganese.

the

low

oxygen

equilibrium

( 2

tephroite

metallic

observe

we

an ex-

two-phase equilibrium tephroite/MnSiO,

Along

medium values of

10"20

activities but also down

_cessof silicon not

at

only

oxygen

tephroite

in

with

low values. Even at

to

a0,

equilibrium

very

exists in

and

7b

which

at

A

second 'critical'

7a

a

activity

Figs.

oxygen

2

is established in

stoichiometric

([Mns¡]

[VI])

tephroite

10"'

composition

with

these

However

and

about

at

in

and

tial

of

Mn304

MnSi03

are

2

respectively

equilibrium

located outside the

IO-2.

wherein

2

points

oxygen poten-

stable and therefore is

is

thermodynamically

discussion.

tephroite

range,

no concern to our

foregoing

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I: The

217

[30]

Point

Electrical

one

of Mn2Si04

Defects of

Conductivity

can

Tephroite.

To

our

be found in the literature

paper

knowledge only

under

which deals

conditions

of

above.

measured

paper

with the electrical

tephroite

conductivity

Another

the

described

concern-

to

ones

comparable

is

Dieckmann

the

The

same

[41].

with

prepared by

subject being

et

ing

of Bai

al.

included

results

are

our own

results

[30]

together

measured

in

8. These authors found the electrical

be about 2.5 times faster than

similar behaviour is known from diffusion

dc-conductivity,

by

Fig.

method

to

[010].

[100]

two-point

along

in olivines

A

[11,

experiments

c-

a-

diffusion coefficients decrease from

Because

where

to

our meas-

to

14],

crystallographic

b-direction.

have been used in

polycrystalline samples

between Bai's conductivities and

urements

a

straightforward comparison

is

we

Nevertheless

have

commented.

be First

not

two

ours

to

things

possible.

of all

have

et

look

to

the

at

of from MnO-

MnSi03

dependence

resp.

small effect

Bai

al. found that activities have

MnSi03-saturated

conduc-

a

on

about 1.6 times

activity.

only

tivities with

samples showing

higher

we

contrast

values than MnO-saturated

found that conductivities

ones.

By

than

are

of MnO-saturated

about

6

times

conductivities of

minimum could be

not

samples

higher

ones.

a

MnSi03-saturated

Secondly,

conductivity

et

detected

Bai

al. which is

that

because these authors

low

not

by

surprising

restricted their

whereas

The

model

are

activities

measurements to

our measurements were

as

10~10,

oxygen

carried

only

out

10~16.

down

to about

et

so

our

defect

as

Bai

al. differs in

three

far from

model,

developed by

these authors take into account

defects which

only

majority

on a

e'

In

and

Mnsi.

whereas

model is based

fourth

7a

and

our

Mn'Mn, Vm„

majority

defect that is

with

results

Bai

7b)

our

(see

Fig.

agreement

et

al.

[ µ„]

that the

condition switches from

propose

[e']

charge neutrality

low activities

the conduction mechanism

2

activities. Con-

at

to

at

[Mn'Mn]

[Vm„]

oxygen

high

Bai

al.

et

at

activities,

cerning

high

give

somewhat different

of their results in

^sofar ^as

a

assume

interpretation

they

completely by transport

that

are

conductivities

carried

at

high

temperatures

whereas

of

motion of h' is

Mn2+

ions via

vacancies,

hopping

contrast to our

mass

responsible

In

et

for conduction low

have

Bai al.

at

experiments,

temperature.

been

action

the

not

able

estimate values for the

of

to

constants

did

we

which

results from

defect

because

could combine

predominating

equilibria,

here with

our

results

our

coulometric titration

given

experi-

which will be

soon

ments,

[34].

published

Acknowledgement

was

Deutsche

This work

financed

the

which is

Forschungsgemeinschaft,

by

greatly apprecitated.

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Point defects of tephroite. I: The electrical conductivity of Mn2SiO4

DOI: 10.1524/zpch.1998.206.Part_1_2.197

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Article abstract of DOI:10.1524/zpch.1998.206.Part_1_2.197

Full text of DOI:10.1524/zpch.1998.206.Part_1_2.197

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