Internal solid state reactions

Prog. Solid St. Chem. Vol.22,pp. 1-57, 1993

0079-6786/93$15.00 ©1992PergamonPressLtd

Printedin GreatBritain.Allrightsre.served.

INTERNAL SOLID STATE REACTIONS Hermann Sehmalzried* and Monika Backhaus-Ricoultt *Institut fiir Physikali~he Chemie der Universitit Hannover, Callinstra~ 3-3A, D-3000 Hannover 1, Germany tLaboratoire de Physique des Mat~riaux CN-RS Meudon, France

Dedicated to Professor Robert Haul on the occasion of his 80th birthday

ABSTRACT Internal oxide both

solid state reactions

systems)

are reviewed.

in respect

are treated.

of theory

Thirdly,

in n o n m e t a l l i c

Firstly,

systems

internal

and experiment.

(in p a r t i c u l a r

oxidations

Secondly,

in

are discussed,

internal

reductions

reactions of type A + B ffi AB which occur in a solid

matrix (~) are introduced

and some pertinent

electrochemical

reactions

internal

examples

are analyzed,

are given.

Finally,

the c h a r a c t e r i s t i c s

of

which are junctions of the type electronic-ionic.

INTRODUCTION Internal

solid state reactions are defined here as chemical processes

curring forms

in i s o t h e r m a l

heterogeneous

in the interior of a solid,

contact with its surface. that has been carefully the past

is the

internal

mainly of a noble metal component face,

when

the

reaction

after a reactant has been brought

both experimentally

reaction

particles

oxidation of metal

alloys.

If the alloy consist

one observes that the oxidation product

(as shown in Fig. BO n p r e c i p i t a t e

front in the interior

i) in a BOn-oxide

layer on the sur-

at an advancing

of the noble metal A

(more or

occur

by forming

heterogeneous

the product

AB b e t w e e n

separates the reactants spatially reaction

is possible

across the reaction

solid

state

reactions

the reactants.

(see Fig.

*To whom c~respondence should be addressed.

In binary

the

sharp)

i).

Some-

in space and [i].

(say A+B In this

= AB)

way,

AB

i), and the advancement of the

only if A, B or both can be transported product.

Rather, less

(see Fig.

is found to be periodic

time, quite in analogy to the well-known Liesegang phenomenon isothermal

in

(A), in which a minor amount of a much less noble

times the internal oxidation process

Normally

into

and theoretically

where the oxidizing agent contacts the reacting system.

product

oc-

product

The first type of internal solid state reactions studied

(B) has been dissolved,

often did not form

systems

systems,

this

in some way

is the only mode of

2

H. Schmalzried and M. Backhaus-Ricoult

(A,B }, z.B. (Ag,A/}

02(gos)

CB

2)

02 (gas)

3)

G OO I OO OoOI (A,B) O 00~ I

02(gos)

ooo:L

°?;,X-

/ 80n

Fig. I. External and internal oxidation schemes for the alloy (A,B). 1) Before oxidation, 2) external, 3) Internal.

heterogeneous

reaction

(due to the invariance

equilibrium),

and this

is well-known

pure metals ant.

(A-O).

In ternary

As a consequence,

reaction.

Thus,

they

systems, may

however,

become

from a morphological

According dation

interfaces

morphologically

of

are vari-

unstable

during

internal reactions

are

in ternary and higher systems,

takes

place

illustrated

in field

in Fig.

I. In the

2, internal

fields

0

A

in local

unstable moving interfaces.

to the Gibbs phase diagram

of an a l l o y

the

point of view,

just extreme cases of solid state reactions with morphologically

of the interface

from the field of the oxidation

B

71g. 2 . Gibbs phase diagram for the ternary system A-B-O.

II,

III

oxietc.

Internal Reactions

similar

internal oxidation processes may also be encountered.

internal

oxidation

systematically first

3

glance,

of n o n m e t a l l i c

in the the

solid

last decade.

underlying

solutions

Although

transport

has been

similar

processes

Indeed,

investigated

in appearance

in the

the at a

reacting

oxide

systems are quite different from those that take place during the internal oxidation of alloys.

The basic observation

is as follows:

An internal re-

action front, consisting of small precipitates of a higher oxide, advances into the interior of the oxidizing oxide solid solution matrix, oxygen potential has been sufficiently From an inspection processes has been

should

of Fig.

occur

oxide systems.

increased at its surface.

2 it is also apparent

in nonmetallic

found and studied recently,

the

as well,

internal

as

indeed

are not confined

importance

of oxides,

electrons

reaction

(or holes)

front.

occur in semiconducting or in mixed conducting crystals,

This

to

we for-

in terms of oxide solutions.

any case, to oxidize or to reduce internally, (or from)

internal reduction

solid solutions

But in view of the practical

to

that

these reactions

mulate subsequently the relevant relations be t r a n s p o r t e d

after the

In

have to can

only

but not in purely

ionic conductors. Another Here,

type of internal

two solids

solid state reaction

A and B which

are both

is i l l u s t r a t e d

soluble

in a m a t r i x

in Fig.

3.

crystal

C,

diffuse from opposite sides into C and form a stable product AB inside. A further type of internal solid state reaction ture.

is electrochemical

in na-

It occurs when an electrical current flows through a mixed conductor

crystal,

in which the point defect disorder changes in such a way that the

transference of electronic charge carriers predominates crystal,

whereas

the transference

is essentially

in one part of the

ionic in the other part.

C

A i

°

JA

s

JB

Fig. 3. Schematic plot of the internal reaction A(~)+B(~)=AB(~). Example: CaO + T i O 2 = CaTiO 3 (in N i O - m a t r i x ) .

4

H. Sclnnaizricd and M. Backhaus-Ricoult

Since in a closed electrical in the transition internal force

solid

circuit the total current has no divergence,

zone from more electronic

state

decomposition

is sufficiently high.

internally,

whereas

The

immobile

the m o b i l e

charge

to the corresponding

driven

internal

to more

reaction

ionic

ionic c o n d u c t i o n

occur, carries

Obviously, only occurs

this

an

if the driving

ionic component

component

electrode.

solid state reaction

must

is precipitated the e l e c t r i c a l

electrochemically

if the applied

voltage

exceeds the decomposition voltage. In the sections which follow, reaction mentioned nucleation about

it.

stage

is not t r e a t e d

But the constraints

exert on the n u c l e a t i o n They

the different types of internal solid state

in this introduction

can

are discussed

in any depth,

because

which the structure

and growth

lead to the formation

little

products

phases

which

The

is k n o w n

of the m a t r i x

of the internal

of m e t a s t a b l e

in some detail.

crystal

are severe. do not exist

outside the matrix. INTERNAL OXIDATION OF METAL ALLOYS Although

this well-known

type of internal

the centre of our interest here,

for historical and heuristic reasons. transport metal the

processes.

solid solution

oxygen

component,

potential

Internal metal (A,B)

solid state reaction

in

Fig. 4 gives the scheme of the main oxidation

and the oxidant

exceeds

is not

its main features are briefly summarized requires

at least a binary

(here oxygen).

the o x i d a t i o n

potential

In general,

of the

less

if

noble

either external or internal oxidation must take place. The bas-

ic parameters which determine the kinetics of the oxidation process in the solid state,

and which therefore also determine whether internal or exter-

nal oxidation takes place, types

(structure,

are:

alloy composition

width of phase fields)

(NB = 1-NA) , number and

of compounds and solid solutions

A(B)

02 {P02 } 000000001

I

oooo o o o oj...... OOOOOOOO o O O O O O O O ~

i C_oO

O0000000J

|

.

BO

I >

I

<.

O

Co I

Fig. 4. Mechanism of the Internal oxidation of metal alloys (A,B) (schematic).

~mmMReacfi~s which

exist

component

in the ternary

Gibbs

chemical potentials of these phases,

individual

mobilities

the reaction products. essary

system A-B-O,

5

of the c o m p o n e n t s

energies

of formation

and

and last but not least the

in both the metal

alloys

and

in

The complete set of those parameters which are nec-

for a quantitative

and predictive

treatment of the internal oxida-

tion kinetics is normally not available. Wagner

[2,3] provided the first predictive theory for this type of inter-

hal reaction.

Internal oxidation of a metal alloy occurs if the less noble

metal B, dissolved

in the more noble metal A, is oxidized

to form the product BO n before B

in the A-matrix

diffuses and reaches the sample surface,

where oxygen is available with a sufficiently high activity. Internal alloy oxidation thus occurs if the oxygen which can also dissolve in t h e

A-matrix

transported met, Cd,

is t r a n s p o r t e d

from the bulk

for example,

if Ag-

faster

interior

into

to the

(Cu- or Ni-)

the

sample

surface.

bulk

Such

alloys with small additions

In, Mg or Si are oxidized in air. As long as diffusional

O and B controls =0 time, tional

(surface)

the reaction

and 9 = m

the inner r e a c t i o n to ~-t. This

negative,

there

negligible

and the

~ F moves

is the p a r a b o l i c

are n e g l i g i b l e

oxygen

kinetics,

(deep in the bulk) front

in advance

than

rate

boundary

is

of A1,

transport of conditions

at

are fixed and independent of

into the A - i n t e r i o r law.

concentrations

of the front,

B is

a situation

If

AG~o

as propor-

is s u f f i c i e n t l y

of B behind the front and

which

conditions

simplify

the

mathematics appreciably.

~F

=

The r e m a i n i n g for oxygen

(l)

2 •u" V~67~

mathematical

between

0 ~

9 ~

problem ~F,

is the solution

and for B between

of Fick's ~F & ~ &

coupling of the B- and O-fluxes at the reaction front tion-independent

diffusivities

of the d i s s o l v e d

second

law

~ ~ with the

~F" For concentra-

species

B and O

in the

matrix A, the solutions are [3]

No/N ~

=

1 -

(erf(~/2.VDo----~))/er

f

u

NB/N~

=

1 -

(erfc(~/2.VDB---~.))/erf(a/VDo/DB

(2)

)

The growth parameter u is found from the flux coupling at obtained numerically from the following implicit equation

(3)

~ F and can be

6

H. $chmalzriedandM. Backhaus-Ricouh

N~.qD-~B.eU2"DolDs.(l-erfa.q~OT~B) In the case that Do.N O >> DB.NB, transport

~F

the parabolic

=

not necessarily independent the

diffusional

rate law reads

(6)

corresponds mean

distributed

to the initial distribution

that the

oxidation

particles

between 0 ~ ~ ~ ~ F, and

B-fraction

process,

precipitate

is also

supersaturation is much higher

and one expects

oxide

does

constant

(i.e.

is needed to nuclein the beginning

therefore

in the near surface

its

in the homogeneous

of this precipitated

size distribution

of ~ ). Because a certain

the rate of supersaturation

internal

smaller

significant

(5)

But the homogeneous

ate BOn,

excludes

42"Do'(S~l~)'t

fraction

alloy.

(4)

e ul

.

(.~I (2.N~)) 2

In this case BO n is homogeneously molar

N~

of B,

=

whereupon

which

=

that more

region

than deeper

of and in

the bulk. Although

occasional

earlier,

systematic

Grobe

observations

of internal alloy oxidation had been made

investigations

[4] and Meijering

tors have measured

started

and Druyvesteyn

with the works

[5].

~ F of the oxidation

Since then,

[7], Fe-alloys

ide layers,

[8], Ni-alloys

zone by metallographic

techniques

[9]).

to qt. Verfurth

and Rapp

in agreement

with

the values

[10] oxidized

determined

thickness

varied inversely with /~In"

A number

of experiments or oxygen

the c o n c e n t r a t i o n creases tion.

has

or decreases.

the

on the

ox-

a series of Ag-In-alscale thickness

by other

techniques.

influence

of abrupt

internal

oxidation

of the precipitation

microstructural [11] and

~Po~

patterns [12]).

reflect

~F' scale

changes

in

Since

to t h e s e

front

The front may even reverse the direction ( dT

The

process.

of O and B have to be a d a p t e d

the velocity

corresponding

these abrupt changes

studied

potential

profiles

conditions,

The

[6], Cu-

In the absence of external

loys and derived the product No'D O from the internal

boundary

(Ag-alloys

the depth of the internal oxidation scale has been found to be

proportional

temperature

and

investiga-

and compared the results with predicted reaction rates alloys

of Rhines many

either

new in-

of its mo-

the response

to

Internal Re,actions

Periodic

precipitation

occur upon the and precipitate conditions

patterns

interplay

diffusion,

if the transport

for periodicity.

found in the literature

in the sense of L i e s e g a n g

between

growth,

7

Details

phenomena

supersaturation,

parameters

meet the

of the m a t h e m a t i c a l

can

nucleation appropriate

analysis

can be

[13,14]. Liesegang bands have been observed during

the hydrogenization of oxygen saturated Ag-alloys under certain reaction conditions. Water bubbles form [15] as well-structured bands. Also in the internal bands

oxidation

are

of Be-,

observed

[16].

Mg-

or A l - d o p e d

In the

latter

silver-cadmium

investigation,

alloys

the

these

influence

of

various reaction parameters on the band distances has been studied. If the t r a n s p o r t

product

the BOn-fraction of t h e

alloy.

eventually

CB'D B cannot be n e g l e c t e d

With

increasing

changes

from

enrichment,

internal

the m o d e

to external.

where

~

(~/2).(N~/N~).(Do/DB).(VMe/VBo).

~ * is a critical volume fraction

alloy volume. Ag-In-alloys

of a l l o y

The condition

transition has been discussed in the literature

N~

(compared to Co'Do),

is enriched near the surface above the initial B-fraction oxidation

of this mode

[3]. It reads

(v)

~*

(e.g.

0.5),

and VMe is the molar

This transition criterion has been tested,

for example,

for

[12]. At T = 550 °C in air, the external oxidation occurs for

N~n > 0.15. This corresponds to an oxide volume fraction of 0.30. For lower oxidizing activities transition observed

(e.g. aoa = 10 -7 , ao~ = p O ~ / p ~ ,

P~z = 1 bar), the

is shifted to lower initial indium fractions

(N~n = 0.02). This

shift is in accordance with the criterion

established by C. Wag-

ner. In many technical low an external available

[17,18].

Pd)-alloys,

applications,

oxide

scale.

the internal oxidation

Analytical

The experimental

solutions

zone is formed be-

of this case are also

test was done on Cu-Be- and Cu-Pt(Cu-

where in air an external oxide scale and the internal precipi-

tation of Cu20 occur simultaneously. The foregoing short remarks may suffice to introduce the phenomenon of the internal oxidation of alloys and to prepare the understanding for internal reactions

in nonmetallic

An o v e r v i e w

on internal

very

early

stages

est,

since

modern

studies

thereof

sion of the change

of

systems, metal

internal

nuclear

is the main task of this article.

oxidation alloy

component

for BO n p r e c i p i t a t i o n

is given

oxidation

spectroscopy

[20]. The recent

solvent

which

could

demonstration

A is also

[19].

be u s e d that

required

has also c o m p l i c a t e d

and morphology of internal oxidation.

in

have gained

to m a k e

short

to

Recently special

detailed

circuit

support

the

interdiffu-

the volume

the expected

kinetics

8

H. Schm~lzried and M. Backhaus-Ricoult

INTERNAL OXIDATION OF OXIDE SOLUTIONS Introducto~ 7 remarks Internal oxidation processes solutions

are a r e l a t i v e l y

systematize

the various

in nonmetallic new field

inorganic compounds

of research

internal oxidation

[21].

Fig.

(and reduction)

and solid 2 helps

processes.

to The

schematic phase diagram A-B-O shows extended ranges of solubility between A and B, AO and BO, and A304 and B304, tion on internal metal esses w h i c h

occurred

respectively.

In the previous sec-

alloy oxidation we have discussed

in the field

I of this

ternary

oxidation proc-

phase

diagram.

The

oxidation processes that take place in field II involve an oxidation of an oxide solid solution rather than a metal alloy. The oxidation process then leads to a higher oxide.

If this oxide product is precipitated internally,

instead of forming an external product layer, the process is called interhal o x i d a t i o n

of the oxide.

It is the c o n s e q u e n c e

intensive state variable oxygen chemical potential

of an increase (~O~

= 2"~O),

of the

at given

P and T, on the surface of the reactant oxide. To discuss

the course

of

internal

oxidation,

a phase

diagram

of second

kind is preferred to the Gibbs triangle of Fig. 2. In the diagram of Fig. 5

the mole fraction N O of oxygen has been replaced by its chemical poten-

tial

(~O=).

In this

way,

one

can

visualize

the

change of the oxygen potential into the two-phase

reaction

path

after

a

field, where the higher

oxide and the initial oxide coexist.

A~

P'o2

P'o2

3

(IogPoz)

(Iogp02l A/./. A J

A

B NslNA÷N8 ~

A

B NBI NA÷NB

Fig. 5. oxidation of (A,B)O. Reaction path plotted in a phase diagram of second kind. a) complete solid solution series AO-BO, b) limlted solid solution series AO-BO.

Internal Reactions

Theoretical

analysis

The k i n e t i c solutions [21].

equations

for the

have been developed

It is assumed

internal

impossible.)

As

(spinel)

For simplicity, um w i t h

oxidation

that the oxygen component

long

as

of

(A,B)O oxide

(sublattice)

is immobile.

the internal oxidation reaction would be

I~GAoI<<

J~GBoI,

the

oxidation

product

the formation of stoichiometric spinel AB204 in equilibrimatrix

scheme is given in Fig.

AO

(NAo =

1)

is c o n s i d e r e d .

6. At the internal reaction front

The

reaction

~F' the (chemi-

cal) reaction consists of the local rearrangement of the cations of cations),

structure

and

This reaction

is

as indicated in Fig. 5b.

a B-deplete~

to a spinel

solid

about one decade ago by one of the authors

(In the case of alloy oxidation, (A,B)304

9

under the

a corresponding can be formulated

influx of cation vacancies flux

of

compensating

MeO + Me30¢

Oo, M

equation

I /

?F

o

1 at ~: --/Ozlg)÷MeZ'=: MeO÷V~e.___,.

at F~F: /.MeO*V~e + h" : Me304÷Me 2"

overall reaction:

3MeO÷ ½0~(g) = Me30 ~

Fig. 6. Mechanism of (A,B)O-oxidatlon. Schematic representation of the diffusion processes involved.

tween components and structural elements as follows

VMe + h" + 2-AO + 2.BO

=

2+ AB204 + AMe

of

defects.

Me= (A,B) MeO

B'.'----I

-_

electronic

in form of a q u a s i c h e m i c a l

(A,B)O

(= outflux

(8)

be-

10

H. Schmalzricd and M. Backhaus-Ricoult

The

lower arrows

that

8

is the

indicate

molecules

AB204

crystallographic

between the two phases

ingoing

(~) and outgoing

are required spinel

unit.

is neglected,

(~), see Fig.

6. Note

to form a 'lattice molecule', For

simplicity,

and accordingly,

which

any volume

change

V~ = i/4.V~ p.

The influence of lattice mismatch and the degree of coherency of the spinel precipitate

on the nucleation

and the growth processes,

and thus on the

initial solid state reaction kinetics are neglected at this point. the spinel volume of the oxidation

iF

=

which

says,

gen,

~/4

that

reaction

As

conservation

of

vacancies

long as

~

= (I-A)'AI,NBNO

2.(N°-N)/(I-2N)

For the last part of eq. the semiquantitative reaction

~

of the front must

attains

of the B-cations

to a high thermodynamic

arrive

the advancement

a constant

yieias,

(steady

(4. (A,B)O

state)

value,

the equa-

+ (~-ions)

2.(N°-N.(I-2.N°))

:

(io)

2.N o

for the spinel phase.

(but by no means strict) given

in

[21].

dl consists of

layer

denotes

coordinate

of the internal

As

of the outer

velocity

is Vm. Jv. The vacancy

surface

long

of

the

as no v a c a n c y

6). The

front,

~ S towards

inter-

sinks

or

~S < ~ < ~F the cation

~F-part

and part

the oxidizing

flux JV corresponds

terflux that arrives at the surface formation of AO. Thus

We will summarize

discussion

two parts:A| = IF + ~S, where

(see Fig.

oxidation

movement

((2+.o)/.o)

1 mole of oxy-

front

(10) it is assumed that N << 1, which corresponds

The total oxidation the surface

the

in view of the local reaction

+ A/4.AB204

stability

kinetics

involves at

sources exist in the crystal, div JV = 0. Between vacancy flux can be formulated as

advancement

zone,

(9)

if the advancement

moles

tion AI_NOBNoO

nal

in the internal

front can be written as

(4.V~/A).jv

~(A,B)304).

=

fraction

If ~ is

stems

~S constitutes gas.

9S

from the the

The surface

to the A-cation

coun-

~ S and reacts with oxygen under the

(Cv_Cv

(12)

Internal Reactions

If we further assume that reaction

law results

&22

=

from eq.

2-k.t

~_

is proportional potential

c~ << c~, a parabolic

;

in AO near the surface. diffusion

and that

(12)

c(2+ o)

--

(5~ • N~)

DV is constant

11

(21

c21

to the self-diffusion

The so-called

which results

coefficient

enhancement

from

of the cations

factor z arises from the

the fast electronic

charge

carri-

ers. The

assumptions

(A,B)O-phase

made,

behind

however, the

(A,B) 304. This spinel, can v a r y i n see Fig.

oversimplify

reaction

front

composition

zone,

the point

defect

diffusion

point defect

thermodynamics rate

the reaction

front

internal

(e.g.

oxidation

of alloys.

and e l e c t r o n

holes

to the role of dissolved

(V~e + 2h', V~e + h') If the volume

nal to internal

of precipitated

oxidation

has been derived

the transition

solutions

(~S)

and at

solid solutions defect

oxidation

process)

Nv¢ s)

•

is

in the metal matrix during

+ O~'. The mobile point defects agent.

exceeds

a critical

for the transition [21]

for alloys

in analogy [3].

value,

from exter-

to the crite-

For oxide solid solu-

the criterion reads

Dr.

with

'pairs'

if we regard the equilibrium

spinel

A criterion

considered.

solid

of the point

oxygen

since the

This is normally true for

oxide

obvious

½ 02 = (V~e + 2.h')

will occur.

rion which describes

in the

in this

observations.

locally act as the oxidizing

fraction

oxidation

role

com-

Cv" In most

at the surface

of nonmetallic

The

atomic

This is immediately

of the defect reaction

external

conditions

of oxide

(A,B)O,

very

constant

for the systems

according to experimental

the internal

alloy oxidation.

gradient,

these considerations,

oxidation

The

spinel

[22]).

factor fv = ~ v / ~ I n

(~F) become time-independent.

oxidation

vacancies

similar

tions,

(see for example

are not available

if the boundary

oxides,

Let us compare

the

become

D v is by no m e a n s

law for the internal

only

semiconducting

thermodynamics

cases we cannot quantify

is expected

the

coefficient

&~

since it contains the thermodynamic

A parabolic

problem.

with

as a function of ~0 while it coexists with

plex in the internal oxidation region

of the practical

transport

which spans the internal oxygen potential

5b. Therefore,

The c h e m i c a l

the

~F c o e x i s t s

¢14)

12

H. Schrnalzrj.(~dand M. Backbaus-Ricoult

where u is a numerical large

compared

factor of the order of one. And since ~

to D B

(because

B is rendered

mobile

through

is always

the thermal

motion of V, and N B is > or >> NV), one may predict that the internal oxidation

of nonmetallic

solid solutions

should be more

common

than the

in-

ternal oxidation of metal alloys. The phenomenon lurgy,

of internal

materials

science

mechanical

properties

hardening.

Internal

phological systems.

evolution

ess is dispersed Let us mention

chemical

zone, however,

reaction

of phases)

another

tential

must

Therefore,

in component

also

change,

under appropriate

advancing trix,

reaction

with

reaction

activity

near the

In addition,

composition, point

in interdiffuinterdiffusion

if during the inter-

conditions,

change because

the local internal

defect

relaxation

the diffusion

(or lower)

the precipitates

NA

t

(A, B ) 30~,

Po2(ext)

(reaction)

oxide

field

again

(see Fig.

r J~....-t >U

~.-'~-I-••• •••

i i' B

(A.B)O' I(A )6" I

(A,B)0equ.

(A,B)30~,

t-0 t>0

(A,B)

no

With

into the ma-

(AB;O' i .B;O"I ~,.

fast.

path in

then occurs.

redissolve

of

oxygen po-

is very

/- %

I ABI', I i1 iI A

proc-

is kept constant at the

as can also be read from Fig. 7.

lao 2

other an in-

rises on the side of the faster moving

of a higher

time,

to the

oxidation

the phase diagram of the second kind runs into a two-phase 7). Local p r e c i p i t a t i o n

multiphase,

in the solid solution matrix.

of the sample [23].

unless

of the mor-

systems

of the internal

(oxygen)

interior

the

by dispersion

In contrast

the local point defect concentrations

the local changes

it alters

than two-component

(for example,

type of internal

the oxygen potential

process

in higher

process.

isolated

possible

In the

because

in particular

of a multicomponent,

the product

cation due to the interdiffusion diffusion

case

phase boundaries

and spatially

surfaces.

patterns

a limiting

sion couples where the metalloid external

mainly

role in metal-

can also be seen in the context

of reaction

with unstable structure

and geochemistry,

oxidation

It constitutes

terwoven

can play an important

of the matrix crystals,

transport-controlled systems

oxidation

t=0

preci pi to t i o n

Fig. 7. Possible reaction path during chemical diffusion in AOBO, plotted in a phase diagram of second kind, with temporary precipitation.

In.real Reactions

ExDerlmental In the

13

results

following

we report

briefly

on the experimental

results

found

in

the literature. (NI,Fe)O ~ NiFe204 + NiO In accordance NiFe204 tion

with

the

phase

in air of iron-doped

and precipitate sublattice. turbed

diagram

is found in the interior are cubic,

Therefore,

during

NiO. with

oxygen

stoichiometric

ions forming

precipitation.

spinel

el unit

cell consists

of both the matrix

a face-centred

remains

However,

is necessary during precipitation of 8 cubic

structures

sublattice

cations

an NiO unit cell containing

almost

The crystal

the oxygen

the spinel

[22]

of an almost pure NiO matrix upon oxida-

undis-

a rearrangement

of the

of the spinel.

subcells,

cubic

essentially The NiFe204

each of which

4 oxygen ions. The spinel

spin-

originates

from

lattice parameter

is

almost twice that of NiO with a lattice misfit of 0.2 %. Therefore NiFe204 grows

topotactically

terfaces

in the NiO matrix

with coherent

[24]. A well defined dislocation

network

or semicoherent

in-

in the interface compen-

sates the misfit and takes up part of the strain energy

(Figs. 8 a/b).

oxidation

grain

between spinel

of polycrystalline

(Fe0.1Ni0.9)O

900 and 1200"C in air results precipitates

tahedral

[24,25].

particles,

shapes are formed

while

boundaries

the grains

(Fig. 8a). A Fe-depleted

the grain boundaries come quite large

lattice,

size

oxidation

layer with

are decorated

precipitates

10 ~m)

with

with

oc-

various

zone of about 2 ~m adjacent to

is free of precipitates.

tween the parent and precipitate have dendritic

in an internal

The grain inside

(average

Due to the small misfit be-

the precipitates

eventually

be-

(up to 1.2 ~m). At 900°C, most of the larger precipitates

shape with dendrite arms which grow in all <100> directions

of the matrix crystal

(elastically

soft directions)

[26].

TEM investigations have shown that all the dendrite interfaces are facetted. The faces along the arms are bonded by (110)-planes, and the tips of the arms

are terminated

by

the dendrite

arms themselves

precipitates

have

octahedral

For most precipitates tected

during growth. (111)-planes. growth, tion.

shape with

matrix.

energies.

Therefore,

Facetting

smaller

particles,

dendritic

shape,

(111)-planes

as

observed

ple, which is constrained

helps to minimize

of the

[28].

have been deis related

the total energy

are exclusively

(111)-planes

(<50nm)

bonded by

during further

in the direc-

of the particle morphology with increasing in t h i n

the octahedral but this

Small

interfaces

of the interface decreases

arms grow at the corners been

large particles,

(111)-faces.

The shape of the precipitates

When the stability

has

For very

the smallest particles

In [27], a transformation

temperature

[27].

are facetted along

even as large as 1 ~m no dislocations

in the surrounding

to the interfacial

(111)-planes

shape

behaviour

films

of

oxidized

seems to be more

may be related

in only two dimensions.

samples.

stable

For

than the

to the thin film sam-

Ostwald ripening and the

14

H. Schmalzried and M. Backhaus-Ricoult

-5

1150

.i IT. °C-~] 1050 1100

I

1000

[

950

900

(Nil-NFeN)I - 6 0 &N=0018 } log 002 ~N=003 Conductivit y - 0 6 7 O N =0093 - 200

,'7 uE

-~-7

-8

I \

7.8

7.4

70

82

"

Fig.

@.

a) S E M - i m a g e

T = 950"C, tare

t = 5.5 hrs,

of a

(Ni0.95Fe0.05)O-sample

in air.

b) T E M - i m a g e

in an a l m o s t pure N i O - m a t r i x

in air of

(Ni0.95Fe0.05)O.

cations,

c)

(Ni,Fe)O,

obtained

metric

Rate

titration

Note

constants from

8.6

i T -~ ' 10 '~ K ]

after

5.5hrs

anneal

the o c c u r r e n c e for

electrical

[25] m e a s u r e m e n t s .

the

, oxidized

at

of N i F e 2 0 4 - p r e c i p i -

internal

conductivity

at T = 9 5 0 * C

of m i s f i t

dislo-

oxidation [29]

and

of

coulo-

Internal Reactions

coalescence

15

of small precipitate particles,

in these experiments,

which have also been observed

may as well be related to surface diffusion

effects

which are important for thin films. The kinetics of the ferent methods.

(Ni,Fe)O internal oxidation have been followed by dif-

Firstly,

tional metallographic

scale t h i c k n e s s e s

cross-sectioning

have been m e a s u r e d

after oxidation.

by tradi-

Secondly,

the con-

sumption of oxygen during the reaction has been followed in-situ by coulometric titration methods ductivity Also,

during

[25]. Thirdly,

oxidation

electrochemical

has

been

with

samples

stabilized

ume,

zirconia

through

consumption internal partial rates

the

in sealed

solid

as the high temperature of o x y g e n

(titration)

oxide scale.

of

reaction

con[29].

state galvanic

electrolyte.

during

current

internal

been

[25]

The cells

Via a pre-

in the cell vol-

oxidation

of the potentiostat.

could

be

The global

of oxygen corresponds directly to the vacancy flux across the

pressures,

in Fig.

the

the oxygen potential was established

and the c o n s u m p t i o n

measured

follow

PO2 = 10 -11 and 10 -0.67 bar

have been enclosed

fixed cell voltage,

to

in-situ coulometric titration experiments have

performed at 1173 - 1273 K between (Ni,Fe)O

the change of the electrical

used

internal

For different

the

growth

compositions,

kinetics

oxidation were

found.

have

been

temperatures

and oxygen

determined.

Parabolic

The rate constants

are presented

8 c.

Although NiFe204

the

electrical

differs

ternally

conductivity

only very

precipitated

of a t w o - p h a s e

mixture

of NiO

little from that of pure NiO and therefore

nickel

ferrite

does

not

significantly

affect

and inthe

overall conductivity of an internally oxidizing sample, the small electrical c o n d u c t i v i t y c h a n g e can be u s e d to m o n i t o r the o x i d a t i o n process. Firstly, vacancies

after the oxygen diffuse

activity

into the bulk,

change at the sample surface,

while the vacancy concentration and con-

sequently the electrical conductivity increases. tation

and the inward vacancy

the reaction front.

is established between the external electron

hole

Secondly,

spinel precipi-

flux is associated with the advancement

An approximately

advances parabolically.

linear vacancy concentration

determines

the

electrical

of

profile

surface and the reaction front,

For a given local vacancy concentration,

concentration

cation

which

the local

conductivity.

By

integration over the sample one obtains the calculated conductivity of the sample, which can be compared to experimental values. measurements typically

by a f o u r - p o i n t

method

In-situ conductivity

for iron contents

between

show the two expected parts of the a(t)-curve

1 and 5 %

[29]. The AC con-

ductivity was found to be independent of the frequency in the range of 200 -

15 000 Hz. Parabolic rate constants have been determined from the perti-

nent

(second) part of the o(t)-curve values.

(Mg,Fe)O ~ MgFe204 + MgO As

in the

(Ni,Fe)O

system,

been also extensively closed-packed ~$~ ~ I - B

internal

studied.

oxidation

Even though

in the

the oxygen

(Mg,Fe)O system has sublattice

remains

during the formation of spinel from the magnesiow~stite

and

16

H. Schmal~e~l ~mdM. Bar.~aus-R.icoult

the cations

redistribute

tion process

in

(Mg,Fe)O,

a very sluggish

perfect crystals, locations

the matrix

cation diffuser

a self-inhibiting

and grain

boundaries

crystals

sen:

in Fig.

(i) as-grown

(3) annealed

boundaries

fraction

at 2100 K in air,

but they turned brown upon oxidation. specimens,

precipitates

see Fig. 9. In type

never be observed.

(2) annealed were

(3)-specimens,

precipitates

due to a massive

homogeneous formation

after oxidation.

green

in type

were smaller

contents,

spinel precipitation.

[31]. An were

cho-

at 1673 K, ao~ = 10 -9 , initially

be o b s e r v e d

Either the precipitates or the

materials

Only in a well defined

could

high Fe3+-starting without

dis-

(Fe2+),

oxidized in air at T =

tion is available) curred,

Therefore,

it In

should play an im-

973 and 1373 K

starting

F£g. 9. SEN-image of (Mg0.99Fe0.01)O, 900°C, t = i0 hrs.

p-size

in [30]).

of 1% FeO and polycrystals

in air between

9. Three different

at 1673 K in air. All crystals

time d o m a i n

of iron and thus (Mg,Co)O

effect can be noticed.

with a starting mole

is given

the oxida-

transport.

with 1-10% FeO have been oxidized example

(see e.g.

sites,

During the precipita-

is depleted

or subgrain

portant role for the diffusional Single

to tetrahedral

for (Mg,Fe)O was found to be different.

tion of MgFe204 becomes

from octahedral

(1) and

(2)

of p-size could

(no TEM investiga-

nucleation

of Fe3+-colour

This could explain

temperature-

of spinel centres

at oc-

the brown colour

Internal Reactions

Because

of s l u g g i s h

diffusion

and subgrain boundaries

in the

17

iron depleted matrix,

(or grain boundaries

preferentially decorated.

from the d e c r e a s e d

morphologies

are

similar

reaction

to the

in the

interior of the sample

and n u c l e a t i o n

(Ni,Fe)O

case.

rates.

Cross-like

Precipitate precipitates

have been observed with arms growing into the <100>-directions lattice

are

The maximum precipitate size within a grain is 2

~m, with a tendency to larger precipitates resulting

dlslocations

in case of polycrystals)

of the host

(minimum elastic modulus in the rock salt structure).

Rhombic sec-

tions with corners pointing towards the <110>-matrix directions are interpreted as an early growth stage or they may correspond to a sectioning of the

cross-arms.

The

overall

'cross'

orthogonal plates situated in the

morphology

is d e n d r i t i c

(100)-host planes,

with

three

reflecting the growth

anisotropy. Transmission

electron

with an initial [32].

microscopy

fraction

In addition

observations

of

of 10 % FeO c o n f i r m e d

which confirms

polycrystals

the d e s c r i b e d

they show that no dislocations

ferent precipitates,

oxidized

morphology

formed between

that the spinel

the dif-

is formed by vacancy

transport and local cation rearrangement and not by oxygen transport along fast diffusion pipes. For short reaction times, lographic cross-sectioning

the oxidation

scale grows parabolically.

5-10 -11 cm2/s at 1173 K, N~e = 0.01,

and oxidation

in air.

in good agreement with that calculated according to eq. are given in Fig.

Metal-

techniques yield a parabolic rate constant k of This value

is

(13). Other values

10. For longer reaction times the observed scale thick-

nesses are smaller than the calculated values. This self-inhibition

is re-

lated to the depletion of the matrix in iron behind the front and was discussed above. A

~I

-7

I

ffl

(Mgl-x Fex)0

E

o "~"

I

x =o.o5 ---

-8

+

" ~ i - .

o

x=0.05

[35]

•

x =0.02

[35]

O × = 0.ol [35]

-9 '~

I

x = 0.02 s

•+- x

= 0.01

[33]

A

= 0.01

[31]

x

-10 -11

I

75

I

8.0

v

8.5 10. ~ K - 1

T

Fig. I0. Parabolic rate constants k as a function of NFe O for the internal oxidation of (Mg,Fe)O in air.

18

H. Schmalzried and M. Baeklmus-Ricoult

The total

internal

oxidation

scale consists

of two parts.

Since for the

formation of one spinel molecule at the internal reaction front one cation vacancy

is consumed

surface,

and c o r r e s p o n d i n g l y

an external

layer of

one cation

arrives

at the outer

(Mg,Fe)O grows on this surface.

contain any spinel precipitates,

It does not

and its thickness is related to the iron-

depleted internal reaction zone thickness by

Evidently the external

layer is very thin. Therefore,

to be used to measure its thickness,

~S" Rutherford baokscattering

trometry has been applied successfully

[33]. For several samples,

tial surface has been marked by Zr or Pt before others no markers have been used.

special methods have

(internal)

spec-

the ini-

oxidation.

For

The growth rate of the outer and inner

layer of the oxidation scale has been measured by subsequent annealings of the sample in air and analyzing with RBS. The RBS spectra have been i n t e r p r e t e d scribes

the

specimen

areal density.

The

as a series

of

interpretation

iron at the external

surface.

the spectra

inner

for the

Thicknesses

identify

surface

initial

summarized in Fig.

fixed

seem

of

inner

to perturb

the d i f f u s i o n

of an activation

Q* = 430 kJ/mol.

The d i s c r e p a n c y

solved in MgO.

in

scales used to

process

and

energy

in MgO.

Consequently,

for the internal

This value neither corresponds to the

is related

(300 ± 125 kJ/mol)

in MgO

to the

for the spinel formation energy,

ent iron solubility

Markers

of

10 for N~e = 0.01 between 1146 and 1389 K [33].

can it directly be related to the Mg-diffusion as expected.

is visible

and outer

and

Parabolic rate constants are

activation energy of oxygen tracer diffusion in MgO

pendences

composition

shows the enrichment

reaction conditions.

interpretation difficult.

The data allow the c a l c u l a t i o n oxidation process:

p r o g r a m which de-

The typical Fe-peak of spinel

scale.

for different

the

layers w i t h

of the spectra

have been d e t e r m i n e d make a quantitative

by a simulation

nor

(250 ± 100 kJ/mol),

(hidden)

temperature

de-

and to the temperature-depend-

At higher temperature,

more

iron can be dis-

the vacancy concentration and also the self-

diffusion coefficient of Mg in the mixed oxide

(Mg,Fe)O also increase with

temperature.

Electrochemical

in-situ

coulometric

formed to study the oxidation of

titration

experiments

have

been per-

(MgI_NFeN)O with N~e = 0.i, 0.07 and 0.01

at 1273 K. The oxygen activity was varied from aoa= 10 -12 to 10 -8 . A parabolic growth of the internal oxidation layer could be confirmed with parabolic rate constants of k = 1.7 2.5"10 -9

cm2/s,

respectively

10 -9 cm2/s, k = 1.9

10 -9 cm2/s and k =

[34]. As expected theoretically,

the parabol-

ic rate constant increased with decreasing initial iron concentration.

Internal Reactions

Furthermore,

in-situ MSssbauer

19

investigations

using a 57Co/Rh source have

been made to study the oxidation of polycrystals with three different iron contents

[35,36]. Before oxidation,

in the magnesiow~stite. additional

(doublet)

the spectra show a singlet due to Fe 2+

After an increase

oxidation time, which is characteristic distribution

which

in oxygen activity

(to air),

an

spectral component becomes visible and increases with

is neither purely

of a MgFe204

spinel with a cation

inverse nor normal.

The area of the

spinel signal increases with the square root of time, reflecting the parabolic rate law. Parabolic rate constants are reported for NFe = 0.01, and 0.05 for different temperatures, decreases

with

increasing

Fe

0.02

see Fig. i0. Again, the rate constant

content.

The

spectroscopically

measured

values are in good agreement with values obtained by coulometric titration [34] or cross-sectioning For v e r y content spinel

special

of quenched samples

conditions

N~e = 0.01)

(low reaction

a periodic

has been observed

[31,33]. temperature

precipitation

[37]. With reaction

of t h e

(900°C),

low iron

Liesegang

times up to 500 h

type

of

(internal

oxidation zone ca. 120 ~m), three distinct Liesegang bands were positioned parallel to the external surface cipitate

size

increased

(Fig. II). Within a single band, the pre-

and precipitate

density

decreased.

The distance

between different bands decreased with increasing ~ . Liesegang type bands form only result

in s t r u c t u r a l l y

of the transport

the s u p e r s a t u r a t i o n precipitates.

which

internal

is now the defect

parts

internal oxidation

pair

of the

in combination

is n e c e s s a r y

The periodic

to the p e r i o d i c agent

undisturbed

processes

crystal.

with

for the n u c l e a t i o n

oxidation

are a of

of the spinel

can be explained

of alloys,

(e.g.V j +h').

They

a slow build-up

similarly

except that the oxidizing

After the

first p r e c i p i t a t i o n

further diffusion of vacancies and electron holes into the undepleted part of the w~stite does not immediately yield new nuclei, saturation product

is necessary

for the spinel

formation.

in the matrix exceeds a critical value

because a new super-

Only

if the solubility

(which includes the excess

free energy necessary to balance the nucleation barrier),

does new nuclea-

tion take place and the next Liesegang band of spinel precipitates forms. Internal

oxidation

of

(Mg,Fe)O at very

very small topotactical

magnesioferrite

low 200 ~. These small precipitates particles

low t e m p e r a t u r e s

~800°C)

octahedra with particle

represent

which give a superparamagnetic

single domain

behaviour

yields

sizes be-

ferrimagnetic

to the material

[38].

ESR measurements have been performed at different oxidation stages to follow the reaction

[39].

In the starting material,

isolated Fe 3+ is located

on cubic sites, while after the oxidation a strong asymmetric iting the characteristics presence

of spinel.

resonance metric

of ferrimagnetic resonance was found due to the

In an early

line is reported,

ferrimagnetic

are given.

line.

line exhib-

stage

of oxidation,

a strong

symmetric

which is explained as a precursor of the asymNo details

on the character

of this precursor

20

H.

•

•

Schmalzried a n d

(Mg m Fe)O

•

~'"~..o$.°. •~ ' A :' • ,e

•

•

•

•

•

•

•

• ~. , to~

•

F e m - - ~,0.... ". " % • , . ' "• " I ' : :."- _ . "" o. • •p • ~ • • • •

M. Backhaus-Ricoult

•

•

e"

•

.

" t--

" ;0

~',

•

""

,

•

d'

"

"

•

"o e

e

• Z". , . ." . .... . •

.

•

• e.oe oe "e;

K •,

!

."

. ' - - , ".

•

eqJ, . •

t~%'.,.

"- ,. " ' .. " "

•

#.. .

•"

• •

eo•o• o~• "o • ,1 • • •

o+ e."

%

:....,. ?..."t...~..,.:.,~: C . " . . . ' . " " ; " • .. 2~ : ", ,, :', "t" ,', :,.. ; ' , ' .,;: :" ' ..,. ~.."')';.'"". :. i. i : : . ".'" ' . . . . . . :'?':"::" ""

02(g)

J

j

20 ~m 11. Periodic precipitation during internal oxidation of (Mg,Fe)O, [37]. From SEM-imaging, T = 900°C, t = 500 hrs, anneal in air.

Fig.

Hardening authors

of

(Mg,Fe)O

[40,41,42].

where high-temperature function

through

internal

A particularly

oxidation

drastic

creep of polycrystalline

of the oxygen

activity.

While

was reported

by several

effect was reported

in

[43],

(Mg,Fe)O was measured as a

the one-phase

material

is charac-

terized by a softening effect due to the high vacancy concentration presence

of Fe 3+,

the two-phase

which is attributed cipitates, tions. cated.

and,

on the

lets and dendrites cipitation

with

within the grains the matrix

a duplex structure

internal

conditions,

different

size material

and maintains

size material,

between

oxidation

consequently,

Large grain

showed

precipitation

hardening

to the formation of stacking faults in the spinel pre-

and to interactions

Depending

morphology

material

in the

precipitates materials

creep properties small

coherent

shows hardening creep

and dlsloca-

with

different

have been fabri-

precipitates

plate-

after oxidation

mechanism.

forms upon oxidation,

For

smaller

pregrain

which creeps main-

ly by grain boundary sliding. In this latter case, the interfacial ties become more important than the matrix properties.

proper-

Internal Reactions

21

Othez oxides Cubic-cubic under

transformations

formation

are

of the spinel

reported

phase.

if mixed

Experiments

(Co,Fe)O

have

is oxidized

been performed

for

polycrystals of (Fe0.sCO0.5)O in air at 1000 and ll00°C [32]. Due to the high cobalt content, an internal oxidation layer with very large spinel particles (~10 ~m) matrix is formed. The

precipitate

morphology

oxides

are formed.

between

1000 and

pure Fe203 face of

was

of composition

becomes

Experiments

1300oc

found,

layer an internal

(Fe0.94Ti0.06)203

more

have

in air.

which

(Fe0.6Co0.4)304

complex,

An external

zone with thin

in Ti-depleted

with

surface

a columnar

(Co0.85Feo.15)O-

if h i g h e r

been performed

exhibited

oxidation

in a

non-cubic

(Fe0.97Ti0.03)O

layer of practically

growth.

Below this

needle-like

Fe304 was detected

sur-

precipitates

[32].

Olivine As internal

oxidation

can occur

cates with transition ticomponent tion

layer depends

nents.

metals

transition

in oxides,

in low oxidation

metal

silicates,

on the relative

If dislocations

it can occur states.

the nature

diffusivities

can short-circuit

only

external.

If no short-circuit

served:

of olivine

Mg 2+ and Fe 2+ diffuse

[44]. At the surface, MgFe204

is formed.

a silicon

The

tions.

internal

The complicated

tion through tridymite,

reaction

enstatite

in the matrix Fe304-

and

oxidation

scale of

layer consists

along

form preferentially

and composition studied

The

nucleate

dislocations,

parallel but

they

dislocations

along

(Fig.

along

disloca-

of dislocation

to

decora-

[45].

very

coarsen

forms some

u-

as products.

(O01)-olivine

remain

and

SiO 2 (or ensta-

normal to the dislocation

while enstatite

of olivine

oxidation

the and

immobile

(Mg,Fe)O

by TEM investigations

or Fe203-precipitate s on dislocations

The internal oxidation

front

is

of a Mg-rich ma-

and Fe304 or Fe203 have been identified

precipitates

oxygen,

Si 4+ remains

products

has been

alternate with SiO 2 lamellae, tributed pockets.

decorated

while

Fe304 and amorphous

tion by taking a lamellar appearance,

dislocations.

for

reaction

phases:

morphology

oxidation

iron oxide

rod-like

and the oxidation

available

free external mixed

The internal

rite).

compo-

oxygen dif-

(Mg,Fe)2SiO 4 the latter case has been ob-

to the surface

trix and different precipitate

Planar

are

reac-

of the different

occurs by vacancy transport to the internal of the various cations to the surface.

During the oxidation

internal

the oxygen transport,

paths

in sili-

In the case of mul-

of the

fusion along these pipes may become rate-controlling

oxidation diffusion

as well

planes

small.

Only

upon oxidaline. They

irregularly

dis-

12) is used in geology to decorate

dislocations

occurs

rapidly

can easily be seen in the optical microscope

and the [46].

22

H. Sclmmlzri~l and M. Backhaus-Ricoult

Fig. 12.

Decoration of dislocations in olivine upon (internal)

oxidation in air [46]. By courtesy of D.L. Kohlstedt

The s t r u c t u r e the o x i d i z e d tates

of the regions

spinel/olivine

are only a few a t o m i c

sharp interfaces.

interfaces

near d i s l o c a t i o n s

by H R E M

has [47].

layers t h i c k and p o s s e s s

been The

investigated

in

spinel

precipi-

atomically

flat and

~mflRocfi~s

The kinetics of the

(internal)

olivine oxidation have been studied

tail by RBS for the oxidation of IIO0"C

[44],

and by in-situ

23

in de-

(Mg0.gFe0.1)2SiO 4 in air between 700 and

coulometric

titration

[34].

The R B S - s p e c t r a

were simulated by using published values for scattering cross sections and by modelling the specimen through several sublayers with different sition. been

At the external

detected

MgFe204.

and

Because

is

surface,

a Fe-peak

interpreted

as

as large

a two-phase

of slow iron d i f f u s i o n

compo-

as the M g - p e a k mixture

in the bulk,

of

has

MgO

the reported

and

Mg/Fe

ratio can only be explained by a preferential diffusion of iron along dislocations,

while Mg diffuses in the bulk. The growth of the external

layer

(~S) is parabolic in time. &

Glass

Since

internal

oxidation

occurs

in c r y s t a l l i n e

similar reactions occur in amorphous sented

on the oxidation

cordierite)

of a Fe2+-doped

in air at 700 - 800"C.

mated to be 3. Oxidized ternal after

surface

of the

silicates.

silicates In

MgO-Al203-SiO 2 glass

sample,

an

oxidized

layer

by s i m u l a t i o n

e l e c t r o n diffraction.

It consisted

of a two-phase

(Mg,Fe)304,

face layer the tained

i00 nm and

of about

by

25 %

Below the sur-

(ca. 1 ~m deep)

con-

(Mg,Fe)304 precipitates of 1-5 nm size.

The g r o w t h

of both scales has been m e a s u r e d

scale were reported. either t h r o u g h surface

by RBS.

Parabolic

According to these experimental results,

the c a t i o n - d e p l e t e d scale,

is thus

rate-determining.

diffusion

(apparent)

layer or t h r o u g h

However,

in view

the

of the

an interpretation

activation energy in terms of component

is not possible.

internal

oxidation

of oxidizable

cations

tant partial step in glass processing. ten glass during the normally

oxidation in

One of the diffusional steps,

aluminosilicate

complicated morphology of the two- or multiphase layers, of the k-values and the

behaviour

for the growth of the inner and the outer

the glass is controlled by cation diffusion.

The

spectra

mixture

(Fe,Mg)-depleted aluminosilicate glass

was estiAt the ex-

(thickness

of RBS

and did not contain any silicon.

was observed and rate constants

oxide

(enstatite-

samples were analyzed by RBS and TEM.

was d e t e c t e d

if

are pre-

The starting Fe2+/Fe3+-ratio

24 h at 770°C)

MgO and 75 %

one may ask

[48], results

'fining',

added to the melt.

gas bubbles.

Apparently,

arsenic

may be an impor-

To remove air bubbles from the mol(III)

The a d d i t i o n s

oxidation

in glasses or antimony

are o x i d i z e d

zones as d e s c r i b e d

taining aluminosilicate glass have been observed.

(III)

oxides are

by oxygen for the

in the

Fe3+-con -

24

H. Sclmmlzrie~!~mdM. Backh.-s-Ricoult

INTERNAL REDUCTION OF NON-METALS Introduction In the previous

section,

the kinetics

lution oxidation have been discussed ess leads to dispersed less dense

external

internal

product

is raised and discussed:

of alloy oxidation

reaction

layer.

and of oxide so-

for the case that the oxidation procproducts,

but not to a more

In this chapter,

Can the reduction

a different

of nonmetallic

or

question

solid solutions

(e.g. (A,B)203 ~ (A,B)304; (A,B)304 ~ (A,B)O; (A,B)O ~ (A,B)) similarly lead to internally precipitated reaction products? If so, these reactions must occur

in the fields

2. One notes

III,

II or I of the phase diagram

that the reaction

(A,B)O ~

(A,B)

shown in Fig.

is the fundamental

process

of ore reduction. Again,

the morphological

instabilities

tually

lead to isolated

internal

ternary

and higher

component

of the phase boundaries which even-

product

systems.

I

precipitates

Fig.

can occur only

13 illustrates

the

in

reaction

CA.B;o

AO A

,U,o2 (log Po2)

BO

B

(A,B) A

B NBIN A+NB

Fig. 13.

Internal reduction: of second kind.

path of an internal appropriate

reduction

reaction.

oxide solid solution

been exposed to a sufficiently of its nonmetallic surface the

(A,B)O-oxide outer surface es,

since

reduction solid

(or another reducible the reduced

The oxygen

(~S) and the reaction

the local

(equilibrium)

the local oxygen potential.

products

in a schematic front

way,

potential (~F)

point defect

surface of the

solid solutlon) form either Fig.

exempllfied

difference

at this 14 shows with

between

induces point defect concentrations

These point defect fluxes transport

nents across the internal reaction scale,

has

(or chemical potential

in the bulk of the reactant.

process

solution.

After the external

low oxygen potential

component),

or they are dispersed

internal

reaction path in a phase diagram

the thickness

an the

flux-

depend

on

the compo-

of which is

InternalRe.~tio~s

25

(A.B)O

( A . B ) 0 ', A

OOO0 OO0 OOO0 OO0

A2 ÷

V", h"

B 2÷

PO2

OO0

•

o-°-o-°o°-o NA(~F) P

At Fig. 14.

Mechanism of the internal reduction of oxide solld

solutions (schematic).

For simplicity,

assume that the anions

oxide solid solutions)

are practically

almost pure metal A is reaction

front,

(oxygen ions for the reduction immobile.

precipitated in

the r e d u c t i o n

the

reaction

(A,B)O

and s i n k s

is a t r a n s i t i o n

disorder

for the p o i n t

metal

type often consists

oxide

zone

~).

is caused by point defect

which compensate each other electrically. act as s o u r c e s

If }dGBoI>>I~GAo~,

reaction

of

then At the fluxes

The surface and the inner front defect

solid

fluxes.

solution

of cation vacancies

(e.g.

For example,

if

(Mg,Ni)O),

the

and electron holes.

The

externally reduced surface acts as the vacancy sink according to the following reaction equation

. VMe + 2 h

.

+ BO

=

B2+ + ½.O2(g )

(is)

II whereas the internal front acts as the defect source for V~e+2 h ing t o

2+ 2+ BMe + AMe

Two m a i n types internal

=

A + VMe + 2 h" + BMe 2+

of internal

reduction

d u c t i o n w h e n the p r o d u c t example

Vm(A)

destroys

can be distinguished:

of sublattices,

the m a t r i x

2)

internal

lattice upon reduction.

by eq.

(A,B)O-matrix within the rigid,

This process

accord-

(16)

reactions

of the second type is described

tated in the lattice.

reduction

with the conservation

•

(16). Metal A

1) reAn

is precipi-

dense-packed oxygen ion sub-

increases the local volume at the reaction front by

per mole of vacancy flux, resulting in correspondingly

large strains

26

H. Scbmalzried mad M. Backhaus-Ricoult

and stresses.

In contrast,

gen ion sublattice

if one, for example,

reduces

remains essentially undistorted

(A,B)304, the oxy-

(case i), except for a

minor change of the distance between the oxygen planes of the two coherent structures.

If the product

particles

grow

large

enough,

this misfit

is

eventually taken up by misfit dislocations. In the model described

by eqs.

(15) and

(16),

the concentration

of point

defects is lowest near the reduced external surface. As a consequence, cationic bulk transport during the course

coefficients

of an internal

are lowest there as well.

reduction process,

grain

the

Therefore,

boundaries

and

dislocations may become operative as faster diffusion paths than bulk diffusion.

Very special

reaction morphologies

are formed,

as described

in a

later section. Formal treatment of internal reduction processes A quantitative

model

of internal

reduction was reported

tion metal oxides with an immobile oxygen ion sublattice.

[49]

are compensated by electron holes as the major defect species forms to the most common situation). other disorder types. of a w~stite phase of dispersed metal.

(which con-

The model can be easily adapted

We briefly outline the kinetic approach

(A,B)O, which

for transi-

Cation vacancies to

in the case

is internally reduced with the formation

The major assumptions are pointed out and results are

discussed. The p r o b l e m has been treated

for the reaction

14. The system of coupled differential

geometry

equations

behind the reaction front has to be solved with ditions.

as shown in Fig.

of transport

before

and

the proper boundary con-

Even in the unreduced w~stite phase before the front, this can be

done analytically

only

for constant

us define the internal reaction

chemical

diffusion

layer thickness as

coefficients.

~ ~ = ~F - ~S"

Let

At the

external surface ~ ~S, the local mass balance can be formulated as follows

iS

=

- (Jv'V~)

=

(JA+JB)

• V~

(17)

The mass conservation of the metal species A reads

o

Co

OO

(18)

Internal Reactions

where

~

volume

27

is the volume fraction of internal precipitates, expansion

-direction. (constant) position

which

has

been

The b o u n d a r y

assumed

conditions

to occur can be read

in the product, ~

(l+u)

perpendicular from

average volume fraction ~ and a (constant)

volume fraction

and

Fig.

is the to the

14.

For a

average metal A com-

N~, one can relate the scale thickness

a~

to the

as

oo

(1-~.).[

~/'[ - rVA .

According

-

(%._~.)

=

~

+~

,,~ - .?,-.~.~

)

to [49], the integral on the right hand side can be approximated

in a linearized

version by the following

expression

(2o)

o~

B.N A /(~NA/~#)~

:

#F J

where B is of the order of one. AS long as the reduced layer consists essentially (N~ ~ i), it follows from eq. (20) that

z/.~

:

1

of almost pure A and BO

(2l)

~'"~/"~'(~"AZ~)~.

+

From the flux coupling one obtains an additional

equation

(22)

which can be incorporated tion i as

A_

~A

(~+~.).VDV..."

"

{

into eq.

1 +

/3 ('I- 14÷4))'V~w/V2"~- Ig~• ~w[~F)1 ~,,_~.).~,,+~)

If ~ ~ 0.5, one expects external a continuous

metal

can be expected

if

one

the

may

changing

induce

phase ~

(21) to yield the average volume

on the surface.

is smaller transition

the initial composition

(23)

.W,,(I,).:~,,

reduction to occur,

i.e. the formation

In contrast,

internal

internal

to

external

(23),

reduction

N~ of the oxide solid solution.

of

reduction

than 0.5. As can be seen from eq. from

frac-

by

28

H. Schmalzriedand M. Backhaus-Ricouh

An example (Mg,Ni)O the

of such a transition

for

metal

~

= 0.3.

layer

has been observed

If some additional

becomes dense

by

external

[31]

in the case of

reduction

(for example by sufficiently

occurs

and

fast sinter-

ing), the contact between the reducing gas and the wilstlte surface is lost and consequently For internal front at

the reaction mechanism

reduction,

however,

~ F can be calculated

is changed altogether.

the rate of advancement

by balancing

of the reaction

the vacancy production

to the

amount of dispersed A, which is formed with volume fraction

I Jvl

= Dr.

v.",

=

The essentlal the vacancy

point is the determination

flux.

and that CV(~S ) << CV(~F),

NV(~F)' i s

of c v (~F)' in order to establish

In the case that a quasi-steady

essentially

one can rewrite eq.

fixed

by the

point

state has been attained

(24) in the following way

defect

thermodynamics

at

~ F'

as

can be seen by the following point defect equilibrium

^ o + 3 . S M e2+

The equilibrium

=

A+BO÷2.~+

condition

C=h') +Vle

(26~

for coexisting metallic A (note that 2.Nv,,= Nh. )

reads

H$C~F)

However,

K • NAoC~s)

the calculation

tion front, tions

=

requires

Since the transport

of NAO(~F) , which is the composition

the explicit

of the component

dependent

(2~

fluxes

coefficients

in

transport

more or less immobile N~O. Then the solution

problem

(oxide)

solid

the reaction

solutions

[30], a general

is not possible.

(DA << DB)

analytical

problem

bolic rate law is obtained for the advance of interior of the sample ( ~ = 2.kt) with

equafront.

are strongly solution

But if the A2+-ions

in the oxide solid solution,

of the kinetic

at the reac-

of the coupled diffusion

in front of and behind

on the local composition

this complex

solution

of are

NAO ( ~ F) =

is straightforward:

a para-

the reaction front into the

Internal Reactions

where

~

is given by eq.

(23). The rate constant

the point defect concentration ty,

and the initial

29

at the front

concentration

k depends

basically

on

(~F) , the point defect mobili-

of cations

of component

A in the mixed

oxide. Internal

reduction

experiments

Several examples of internal oxide reduction the literature. tions

We will briefly

and subsequently

with reactions

discuss

of type

tially conserved

summarize

studies have been reported

the results

some technical

of these

applications.

(1), for which the oxygen

ion sublattice

example is the reduction reaction

The phase diagram o f second kind for the AI-Fe-O

in ref.

[24].

Almost

stoichiometric

spinel

FeA1204

system

within the alumina-rich

The reduction

has been studied with single crystals

process

with

material

grain boundaries. (1-2 ~m),

At 1450oC,

size

of 10-20~m

Their elongated

Spinel precipitates with essentially

and at 1277"C tals were

reduced

reduction

layer of variable

[51].

shape

(Cr,Fe)203

Spherical

spinel

thickness

~ Cr203

(Crl_NFeN)203

[24].

inhomogeneously

A similar reduction reaction of type sesquioxide

observed,

within the grains

the

product

spinel was distributed

Let us now turn to internal stroyed

(type

(2)).

process

(Mn,Fe)O -- MnO +

in 1962

[53]. Again,

The

starting

cipitates were observed,

of the

dense

proc-

sesquioxide, zone

the oxide matrix

example

reaction

and the Fe-depletion

by X-ray measurements.

ear, which was explained

in which

[51]. is de-

has already

samples

been studied

were hampered by the were used.

Fe-pre-

of the oxide matrix could be

The reaction rate law was apparently

by a slow interface

Due the

is the ore reduction

kinetic conclusions

and not fully

is the

range of 1300-1400"C.

in a broad reaction

interesting This

in a

15.

composition

polycrystalline

reductions

(Fe,Mn).

observed

0.1 and 0.2. The reduction

irregularly

quantitative

fact that polycrystalline confirmed

sintered

A technical

were

(1) that has been investigated

ess took place at aol = 10 -9 in the temperature of

smaller

(aoz = 10 -9 )

Fe-doped alumina single crys-

is given in Fig.

+ FeCr204.

low d e n s i t y

At 1400°C

at

in the

, the size of the spinel parti-

was N = 0.025,

to t h e

Spinel precipi-

preferentially

are appreciably

precipitates

~

cles ranged from 0.1 - 1 ~m. An example

reaction

(aoz < 10-8).

were

[51] and with (A11_NFeN)203

shape results from fast transport

spherical

(ao~ = 10-11),

matrix of the sesquioxide.

polycrystalline

0.1 and 0.15 has been reduced

an average

boundaries.

[52].

is given

is formed upon reduc-

tion and precipitates

tates

is essen-

(AI,Fe)203 ~ AI203 +

FeA1204.

with N = 0.05,

Let us start

(except for the packing sequence).

A well investigated

polycrystalline

in

investiga-

reaction.

Without giving

linany

30

H. Sclamalzried and M. Backhaus-Ricoult

Fig. 15. Sample cross section (SEM) of internally reduced (AI,Fe)203. (Starting material (AI0.gFe0.1)203; ao~ < 10-8; T = 1400"C; t = 50 hrs).

details,

it was

also m e n t i o n e d

(Mg,Ni)O had been observed.

that

The

internal

internal

reduction

reduction

of

of

(Mg,Fe)O

(Mn,Fe)O was

and

later

investigated in detail in [50]. In this

study

(FeNMnI_N)O single crystals with N < 0.2,

with N = 0.i - 0.9 were reduced at 800 - 1000°C. were established reduction riched

by the Mn/MnO solid buffer.

product

matrix.

is basically

For

oxide

The

and polycrystals oxygen activities

From the phase diagram,

pure Fe, which precipitates

single

crystals

and

the

in the Mn-en-

low reaction

temperatures

(800°C), metal precipitates seem to form only along - and -oxide dislocations. imum size tions.

At high reduction temperatures,

1 ~m)

form

in the volume,

At the external

layer with very

surface,

and

spherical precipitates

less f r e q u e n t l y

no continuous metal

large metal precipitates

by Engell aries

along disloca-

layer but a two-phase

is observed.

crystals give quite different results upon reduction. temperature

High density

become

while

decorated

at a lower temperature with

iron.

Intragrain

poly-

At a high reduction

(1300oC), metal precipitates exclusively at pores [53]),

(max-

(800°C),

(as observed

the grain bound-

precipitates

are not ob-

served. The internal reduction kinetics in this temperature range are investigated by scale both

and t h e r m o b a l a n c e

methods

are

in good

measurements agreement

on single

(thermobalance

crystals.

Results

measurements

of

yield

Internal Reactions

slightly for

higher values).

1000"C

with

rate d e c r e a s e s the r e a c t i o n

In Fig.

increasing

16 the reaction

metal

as p r e d i c t e d

rate c o n s t a n t

31

content

rate constants

up to NFe

by the model.

For NFe

= 0.1.

> 0.12,

are given

The

reaction

an increase

in

is observed.

12

I

I

w

'5 ..,

10-

o

O

x=00455

+ x = 0 0705

,.,,," <3

8 -

• n

x : 0081 x = 0097

•

x=OlOZ.

C~

/

/

//

+

[]

2

/.

I

I

6

8

=

[t. h -+]

Fig. 16. Reduction layer thickness as a function of time. (Mnl_xFex)O single crystals reduced with a Mn/MnO-buffer at T = 1000oc.

Tracer [50]

diffusion

allow

[54]

and

one to c a l c u l a t e

w h i l e the e x p e r i m e n t a l The

most

were

extensive

reported

crystals

with

in

studies

[31]

on

content

0.005

Me

of

type

(NMe) which

and the

metal p r e c i p i t a t e s

results are

which results

ions.

Single

~ NMe ~ 0.2 were

reduced

For NMe =

become

can hardly be d e f i n e d in an

located

increasing

deeper

sample

after

in an oxide matrix 0.01,

the distances

(10 ~m)

17a).

and a re-

I n c r e a s i n g metal

precipitate are

atmos-

thickness n~

larger

(Fig.

average

in the

(2)

= Fe,Co,Ni.

size.

less numerous,

Prebut

from the slowing of the b u i l d - u p of the M e - s u p e r s a t -

corresponding front.

decreasing

For s u f f i c i e n t l y

rate high

of n u c l e a t i o n

metal

tates coalesce with sometimes p e c u l i a r m o r p h o l o g i e s JPS~ ~ : l - C

processes

where

are r e g u l a r l y d i s t r i b u t e d

of the nobler metal

layer t h i c k n e s s

reaction

reduction

systems,

layer has a u n i f o r m

the i n d i v i d u a l

vancing

metal

the reaction

between

uration,

internal

in poa (Fe,FeO)),

10 -9 cm2/s.

0.1,

duction

larger,

of

(Mg,Me)O

Metal p r e c i p i t a t e s

Me-content

(N = 0.i

coefficients

from 1000oc ~ T S 1400oc in a C / C O - b u f f e r e d

is d e p l e t e d

cipitates

k = 4.5.10 -9 cm2/s

diffusion

ranging

For NMe ~

reduction. which

chemical

value is found to be 5.2

a transition

at t e m p e r a t u r e s phere.

extrapolated

content (Fig.

at the

the

17 b).

ad-

precipi-

32

H. Sclmaalzfied and M. Backhaus-Ricoult

Fig.

17.

Internal

fractions N~e.

b) "~i

reduction of (Mg,Me)O with different T = 1400°C,

= 0.2, c) "~i = 0.3.

C/CO-buffer,

initial

a) N~i = 0.1,

Internal Reactions

Many

different

they d e p e n d

shapes

partly

of the

individual

on the s p e c i f i c

shape to depend on the transport the

interracial

preferred,

energies.

For

cipitates

were

preferentlal

Me.

coefficient isotropic

for certain reaction conditions of

precipitates

metal

but have been seen in the

For reduction

33

The

Rhombic

formation

of this

Fe-precipitates

tate

A preference

shape

for

and kinetic

plate-llke

shape

always point

have cubic

[55].

shapes

are

upon reduction

shape,

are

only

(110)-MgO

metal pre-

attributed

to

[31], which are

in the <101> direc-

(101)-planes

[31].

ones

multi-faced

larger

become

interfaces

coefficients

are t e m p e r a t u r e - d e p e n d e n t ,

was

soft directions

while the interfaces

the energies

octahedral

system

(Mg,Fe)O,

Cu- and Ni-preclpitates Since

the p a r t i c l e

[31,55].

tion of the MgO-matrix, polyhedra

been observed;

the stress tensor and

systems,

growth along the elastically

<100> and <101>.

have expects

tensor,

(Mg,Ni)O

(Mg,Co)O and in part for

observed.

One

which

was

observed

determine

one e x p e c t s

Small [56].

the precipi-

(equilibrium)

shape

changes with temperature. If Me 2+ is not homogeneously experiment, (Mg,Ni)O, rates

complex

perpendicular

is related

point

the external

of dislocations

surface.

[57].

the situation Those

Metal

experiments

columns

with

They grow individually metal

precipitation

methods, vealed

small

(10 nm)

spikes

have a high

tion 4.2 does not account here,

since

paths to the external er.

More q u a l i t a t l v e (Me = Cu,Fe,Co,Ni)

degree

of which

[58,

59,

(Mg,Mel,Me2)O

grow

branching,

them by conventional was

1 ~m.

TEM re-

in between

may have also been caused

the kinetic model as explained reduction

is found

complicated

in a strict

formation

provides

in the work on

Small metal

bulk. but no

analytic

However,

to grow

the by

in sec-

cases.

As

sense does not fast

(Mg,Me)O

precipitates

is

Me 2 = Fe

into the

diffusion

which is in contact with the reducing

60].

with

form along

with Me I = Ni,

Ni-precipitates

the p r e c i p i t a t e

information

if

with some dendritic

internal

surface,

From a

that pores

of porosity

for these morphologically

we have pointed out before,

form at

one is dealing here with

more complex

been performed

Clearly,

which surface.

is now connected

this means

of

This morphology

and microcracks

But these particles

the coollng of the sample.

prevail

still

rectangular

[55].

17 c).

location

be seen between

resolution

For

in most of the reacted sample.

and isolated,

could

the spatial

dendritic

becomes

[57].

of the Ni-precipi-

and the development

(Fig.

Strictly speaking,

of a reduction

develop

to the e x t e r n a l

Since VMe < VMeO,

form of external reduction

Obviously, reduced.

paths

of view each precipitate

with the reduced precipitates. a special

surface,

to the surface

fast d i f f u s i o n

can

is an alignment

(100)-crystal

parallel

to the presence

providing

transport

to the

bands

in the beginning

morphologies

the effect of a NiO-gradient

precipitation first,

distributed

precipitate

were

buff-

reduction obtained.

34

H. Schmalzried and M. Backhaus-Ricoult

They are homogeneously annealed

at 1923°C

distributed

in Mg-vapour,

The microstructure

throughout

the reduced

or at 1173°C

in graphite

if it is

under N2-flow.

of the reduced samples has been studied by TEM. Neutron

scattering was used to confirm the lattice constants relationships

sample

and the orientational

found from TEM.

At this point we should mention the formation of internal reduction with multiple multiple

subscales.

subscales,

In analogy

internal multiple

to e x t e r n a l subscales

tarnishing

layers

layers

ponent A can exist in various valence states in the oxygen potential of the experiment, tion front. ferent

i.e.

between

Consequently,

suboxides

oxygen potential.

at different

of A are stable,

activity

tates have to transform accordingly A multiple tion of shown

subscale

(Mg,Cu)O

in Fig.

the valence

first reaction

range

inner reac-

to the prevailing

step the highest reduction.

decreases

During

behind

suboxide

diflocal

should

the advancement

it, and the precipi-

into lower suboxides

or into metal.

formation has been studied in detail during the reduc-

[56,

61].

A schematic

18 a, demonstrating

state

and the

depths of the matrix crystal,

front by internal

the oxygen

surface

corresponding

In the first reduction

form at the reaction of the front,

the external

with

can form if the metal com-

I and thus

step,

phase

diagram

the possibility

kind

is

for copper to occur

of second

in

to form Cu20 by internal

Cu20 precipitates

at the reaction

reaction. front

In the

if ao~

< a~a

(CuO,Cu20) . Since the local oxygen activity decreases with time, Cu20 precipitates

are reduced to metallic Cu if aoa < aOm(Cu20,Cu),

see Figs.

18 b

and c.

Io

Po2

CCuM . gplo2 y0-

-lMg.CulO I I

step I

(Cu,Mg)20-~at

MgO MgO-Cu Cu~O (Mg,Cu)O h" • I o

• "v~ • ;

Oo

•

0

•

••

O0.

• MCJ* •

P~2 II

global " reduction

II II

step" 2- 4n II

_L.__

Cu

Cu12Mg CuM2g

•

•

oOoOo 0

QO 2

-Cu2" Mg 2. •

0 °

Oo2{bulk)

O~2)

0~2

Mg

ao2 (surfocel

Fig. IB. a) Schematic phase diagram of second kind of the system Cu-Mg-O. b) Schematic reaction scale of the reduction of (Mg,Cu)O.

In~rnal Re.actions

35

c) Reduction scale of (Mg0.97Cu0.03)O at 1400"c in a C/CO-buffer, t = 9 h r s . S E M . d) TEM-image of the two reduction subscales of Fig.

18 c. On the upper

right

side

C u 2 0 - p r e c i p i t a t e s , low

dislocation density. On the left side metallic tates, high dislocation density.

Experiments The

outer

range

of

(T = 1000"c, scale

0.1

ao~

consisted

- 1 ~m,

while

= of

10 -10 ) h a v e metallic

in t h e

inner

confirmed

copper scale

copper precipi-

this

behaviour

precipitates Cu20

in

precipitates

the

[61]. size

dominate.

36

H. Schmal~iedJmdM. Backhaus-Ricoult

Both Cu and Cu20 precipitates corners.

At higher reaction

not be observed a one-step

have approximately

temperature

[62]. Apparently

reaction mechanism

cubic

(1400°C,

shape and rounded

ao~ = 10-16),

the fast advancing reaction

leading

immediately

Cu20 could

front prefers

to the formation

of me-

tallic Cu in the MgO-matrix. Finally,

internal reactions

and in ceramic materials, are exposed From

to low chemical

a geochemical

(Mg,Fe)2SiO 4 or phenomena since

point

potentials of

view,

oxygen

and ceramic solid

is n o w

interest.

replaced

metalloids.

solutions

such

One expects

as in the oxide solid solutions

anion

conditions

solid solutions

of the corresponding

silicate

(Mg,Co)2SiO 4 are of great

upon reduction

the

should also occur under geochemical if extended mineral

by t h e

discussed

stable

as

similar above,

SiO~--anion

groups. Internal reduction kinetics Only a very limited

number

reduction reactions.

For various

kinetic measurements

have been performed

reduction

temperatures

19 shows

the reaction

from experiments C/CO.

of kinetic

has been done on internal

(Mg,Me)O-systems,

and reducing layer

studies

atmospheres

thickness

where Me = Fe,Co,Ni,Cu,

for different

n~

Me-mole

as a function

of qt,

at 1400°C when the buffer of the reducing

Approximate

(parabolic)

rate constants

fractions,

(oxygen potentials).

are determined

was

for the

fol-

(Mg0.99Fe0.01)O

~ MgO + Fe

k = 1.5 • 10 -9

cm2/s

[31]

(Mg0.91Co0.09)O

~ MgO + Co

k

=

2.0

•

10 -9

cm2/s

[31]

(Mg0.82Ni0.18)O

~ MgO + Ni

k

=

4.0

•

I0 -~

cm2/s

[31]

(Mgo.97Cu0.03)O

~ M gO + Cu

k = 4.0 • 10 -10 cm2/s

[62]

'E

= 200 /

I I

/

/

/

/ ,"

100

++/] ( i ~

•

"

'~

I

5

10

15

20 --m-

•

I

I

25 30 tII2110-1sec -I)

Fig. 19. Reduction kinetics of (Mg,Me)O. T = 1400"C, buffer: c/co. •

O •

: (Mg0.99Fe0.01)O : (Mg0.91Co0.09)O : (Mg0.81Ni0.19)O : (Mgo.97CUo.03)O

obtained

atmosphere

lowing systems

!

Fig.

Internal Reactions

In-situ

MSssbauer

investigations

(Mg,Fe)O

[35]

After

spectral

line appeared

•

the

iron metal

line.

in oxygen

in addition

to the

(unresolved)

as well.

quadrupolar

the perfect cubic symmetry High

dislocation

been observed

to metallic

and

Fe2+-singlet.

densities

self-diffusion

related

caused

to these

electron

coefficients

their

dependence

k-values

agree

than with oxygen self-diffusion the r e d u c t i o n

grew

reduction,

to the existence

strain

fields

[35].

of

fields.

have

already

For Mg 0. 85Feo. 15'

from -12.1 to -18.5 the rate

better

with

are not well-known

bulk

cation

process

self-diffusion

coefficients•

in (Mg,Me)O-systems is c o n t r o l l e d

or

However,

a bet-

does not necessari-

by c a t i o n

diffusion,

which is evident

if one takes into account the complex scale morphology

discussed

For an outward oxygen diffusion,

above.

ties are available:

1) Diffusion

inside the metal or along the along

one-

boundaries)

which

metal/oxide

defects

form d u r i n g

Observations TEM-studies

(dislocations,

cluding

are expected

small

process. ~V

to be faster

= Vm(AO

than

either

2) Diffusion angle

of the reduction morphology,

interface

For the reduction

scale give

size,

and on orientation

information

chemical

relationships

) - Vm(A ) . All

the ordinary

bulk

composition

(of

of

(A1,Fe)203

and the formation

quence),

of the microstructure

studies

The samples were polycrystalline;

matrix

and

and product,

in-

of spinel precipitates,

(except for the packing have

been reported

at grain boundaries.

about

an order

dered

the precipitate

the two adjacent

of magnitude

Intragranular

smaller.

shape disc-like,

grains,

with a different

which may indicate were

[63]. formed

spinel precipitates

Fast grain boundary a special

tionship between matrix crystal and precipitate. interfaces

se-

NFe20 was between 5 and 10 %; the reduc-

tion took place at 1450°C and ao ~ 10 -8 . The spinel product FeAI204 preferentially

crys-

structures.

anionic sublattices

detailed

on precipitate

between matrix

which oxides have similar

semicoherent boundaries)•

grain

3) D i f f u s i o n

of the m i c r o s t r u c t ~ e

tallography, product)

paths

precipitate,

interface.

the p r e c i p i t a t i o n

along cracks which are due to the volume change these transport diffusion.

as

the following possibili-

along the continuous

(porous)

or two-dimensional

a

of the ions in these solid solutions,

the

that

line

,

by the destruction

on composition,

coefficients

ter agreement of k- and DMe-values

of

10 -18•5

.

by local strain

microscopy

understood,

ly m e a n

reduction This

This has been related

interaction,

around the iron nuclei

by transmission

in particular

the

to ca

iron, but it was broader than the

one found at 1000"C and a change in log ao1 constant to be k = 7.2.10 -11 cm2/s. Although

for

activity

During the first stage of the internal

the Fe 2+ signal broadened of an

reported

decrease

with time and was attributed normal

were

37

transport

growth

The dislocations

found to be dissociated

rate

orientational

were reninto rela-

of these

(as in spinel

grain

38

H. Schmalzri~l and M. Backhaus-Ricoult

Intragranular the

spinel

well-known

precipitates

orientation

spllsesq),

were found,

of a FeAI204 particle entational cording

relationship

for which

lel, could not be detected sublattice

have preferred

is

patterns.

but and

are paral-

of the oxygen

energies.

is shown in Fig.

(011)spll(440i)ses q and

to the diffraction

planes

rotations

the misfit

in the alumina matrix

relationship

oxygen

Instead,

which may minimize

directions,

((lll)spll(0OOl)ses q

the dense-packed

in this study.

growth

An example

20. The ori-

splIsesq

The precipitate

is surrounded

ac-

by an

array of curved dislocations

which compensate

the misfit across the semi-

coherent

interface

(spacing

= 9 nm).

set of misfit

(spacing

= 5.8

is found which

nm)

Another

is r o t a t e d

dislocations

60 - 90" r e l a t i v e

to the

first one.

Fig. 20. TEM-image of a spinel particle inside internally reduced (Fe0.1AI0.9)203. T = 1360°C, t = 48 hrs, aoz < 10 -8 .

Detailed

TEM-studies

are also available.

on internally For

(Mg,Ni)O

reduced

(Mg,Me)O,

Me = Ni,

[59], the cubic Ni-metal

Co and Cu

precipitates

in

the internal reduction zone were exclusively topotactically oriented. This observation was confirmed later at 1000 and 1400oC [55], and the precipitate morphology tures,

sometimes

branches detected.

with

tree-like

the

reduction

Ni-agglomerates

conditions. formed,

only 10-100 nm sized cubic precipitates These

the cooling with

changed

very small precipitates,

process.

(111)- and

At high

(110)-surfaces

however,

temperatures,

while

with

At

low tempera-

in between

the

(100)-surfaces

were

could also result

from

large polyhedric

precipitates

were seen in addition to smaller octahedra

Internal Reactions

39

and very small cubes. The precipitates are interconnected by dislocations, and large strain fields are observed around the metal precipitates the

large

lattice

misfit

between MgO

and Ni,

which

are the

due to

coexisting

phases in the reduction zone, as has been confirmed by EDX-analysis. In the case of C u - p r e c i p i t a t e s have an average (lll)-planes

formed

in NiO

size of i0 nm at 1600°C.

[65],

the metal

The surfaces

polyhedra

are preferentially

and show again the cube on cube orientation.

The

interfaces

are semicoherent with a regular network of misfit dislocations. For the internal reduction

of

(Mg,Cu)O the microstructural evolution upon aoz = 10 -17 has been stud-

aoz = i0 -I0 and at 1400°C,

reduction at IO00"C,

ied in detail for single crystalline material with a copper starting content of 3 - 5 % [61, 62]. In all cases, inner subscale with Cu20-precipitates copper precipitates. copper and cuprite tion front,

Depending on the reaction temperature, coexist

is more or less extended.

the zone where

Ahead of the reduc-

no dislocations were observed in the mixed oxide.

behind the front,

a dislocation network of Mgo-type

established between the precipitates. ly low in the

inner

subscale,

are interconnected, precipitates, of small

the reduction scale consists of an

and an outer subscale with metallic

see Fig.

where

copper

cubes

dislocations

was

The dislocation density is relativespherical

0.i ~m-size

Cu20-particles

18 d. In the outer scale with the metallic

in addition to large

dislocation density

In contrast,

0.i ~m copper

formed during

in this subscale

further

cubes,

reduction.

a large quantity Consequently,

the

is so high that it disturbs even the

MgO lattice. During reductions above the copper melting point, per particles itate

lattices

( 500 nm at 1300°C), can be lost.

copper

melting

point,

well

are in the cube on cube

[62]. For reduction temperatures below the

defined

established between the two phases quency of the different

the alignment of the matrix and precip-

Smaller precipitates

orientation at this temperature

for large spherical cop-

special

orientation

relationships

are

[61]. Considering the type and the fre-

orientation relationships,

a model

for the mecha-

nism of the (Mg,Cu)O r e d u c t i o n has been proposed. In a first step, Cu20 can form topotactically (misfit ~ 0 %), or in three distinct orientations. During

advancement

of the front the

Cu20 becomes thermodynamically transform

by loss of oxygen

local oxygen a c t i v i t y d e c r e a s e s

unstable.

into copper,

Domains of the Cu20 precipitates maintaining

Since these orientations show a large misfit, ranges by diffusional lattice.

transport,

equivalent

Cu20 can t r a n s f o r m

copper.

low temperature

At

(14 % misfit).

their

the copper precipitate rearis e s t a b l i s h e d

only at high t e m p e r a t u r e s

the copper metal

orientation.

formally to a rotation of the

In this way a low energy twin o r i e n t a t i o n

Topotactic

and

[61].

into topotactic

is not formed topotactically

40

H. Schmalzricd and M. Backhaus-Ricoult

Remarks on applications In metals and in ceramics,

the presence of a flnely dispersed second phase

in a matrix crystal changes many of its properties significantly.

Internal

reduction is one means to bring a second reduced phase into a matrix crystal under isothermal conditions. Most notably,

internal

reduction

can

lead to drastic

changes

in optical

absorption and colour. Appropriate glasses and crystals could be coloured, be it that transition metal ions lower their valence reduced

precipitates

scatter the

light.

been reported for internally reduced pure MgO

absorption

studies

the mechanical

[60].

reduced

(Mg,Ni)O crystals do not

properties

A 50 % - i n c r e a s e

of

internally

in the d u c t i l i t y

and

reduced

an

Apparently the small coherent metal precipitates

location motion and the crack formation, hardening.

by

internal

reduction

in the

after re-

hinder the dis-

as is known for normal dispersion

Similar effects have been reported by other authors

By and large, the possibilities to establish technical ties

(Mg,Me)O

increase

yield strength by a factor 3 - 4 was found at room temperature duction.

have

of ~ > 2 ~m, but absorb strongly at ~ < 2 ~m. The same au-

studied

samples

or that small

(Mg,Ni)O [60]. The energy band gap of

is 7.8 eV, while the dark-blue

absorb waves thors

Optical

state,

of n o n m e t a l l i c

solid

[66, 67].

interesting proper-

solutions

have

not

yet

been fully exploited. INTERNAL SOLID STATE REACTIONS A + B ~ AB Introduction In the previous ered w h e n

sections

a homogeneous

internal solid state reactions have been considsolid solution

has been exposed

surface to a change of a component potential. inhomogeneous nents

at the external

In this chapter we consider

solids in which diffusional transport of two or more compo-

in the m a t r i x

crystal

gives

rise

to a c h e m i c a l

reaction

between

these diffusing components and leads to compound formation within the host matrix [68].

Reactions of this type are well-known in liquid media. Ag + a n d

medium um,

Cl-

ions are s e p a r a t e d

(e.g. water + gelatine),

down

overlap

(or CrO~-)

their

concentration

and supersede

(or Ag2Cr204).

If the

product,

trix, or three phases have to be contacted: separates

supported

reactant

in a solid,

of AgCl

either

the

in a special way in the ma-

the crystalline matrix C which

two phases which serve as sources

of the reactants

and B, which must exhibit a certain solubility and diffusivity trix C

aqueous

concentrations

they form crystals

this type of reaction

reacting components are initially distributed spatially

If two solutions of

the two reactants diffuse into this medigradients.

the solubillty

To realize

by a w e l l

A

in the ma-

(~). During a high temperature anneal A and B can diffuse into the

Internal Reactions

(separating)

matrix,

41

driven by their chemical potential gradients.

as the solubility product of the compound AB is exceeded somewhere matrix phase

which

means

AB b e c a m e

that

the G i b b s

available

energy

for the

locus,

the n u c l e a t i o n

at this

formation

As soon in the

of the

new

of AB and

its

growth inside the solid host matrix is expected. This type of internal nical

applications.

introduction teresting

solid state reactions may Since these reactions

of AB-precipitates

local changes

lead to interesting tech-

are taking

can lead to special

of mechanical,

electrical

locally,

the

local properties.

place

In-

or optical

properties

inside a matrix crystal may result. Formal description

A theoretical treatment of this internal reaction problem has been recently given in [69]. For ternary A-B-C system, compounds such as oxides,

carbides,

A, B and C can be elements or

etc. The solubilities of the reactants

A and B in the matrix C is limited.

A and B do not form stable compounds

with C (but they may form compounds with C which are less stable than AB). The stable compound AB has a highly negative Gibbs energy of formation. phase diagram Fig.

for a potential

candidate

of internal

21. A and B are assumed to be mobile

experimental diffusion

set-up

anneal.

(Fig.

in C

3), A and B diffuse

Since the boundary

of the reactant sources are fixed,

(~).

reaction

is shown

A in

In a one-dimensional

into the matrix during the

conditions

at the moving

and the component

interfaces

fluxes of the compo-

nents can be written as

j~

~t =

-

Di

•

V ci

(assuming q u a s i b i n a r y profiles), in [69]

behaviour

the diffusion

reaction times,

;

=

A,B

(29)

even in regions

of s u p e r p o s e d

of A and B can be treated

the solutions

for a semi-infinlte

instead of the solutions

complicated.

i

separately.

A- and BFor short

geometry have been used

for a finite s y s t e m which are far more

The concentration profiles of A and B in the matrix of C

have been evaluated.

For constant chemical diffusion coefficients,

tains

CA

=

cB

=

~

'"

(l-erf

4-

~

)

(30)

'

(~)

one ob-

(31)

42

H. Schmalzricd and M. Backhaus-Ricoult

For chemical

diffusion

coefficients

sponding concentrations

which

(D i = D~.ci)

are proportional

to the

corre-

one has

(32)

cB = c~ .( ~,,~ -~,~.Cl-~)~,,~.,J~-""""~:~.~- ( 1 _ ~ ) 2 / ~ . ~ . t K A = (k11~)l12 + ( 6 + 4 W q j ~ ) 1 1 2

;

The latter results are particularly erovalent reactants, tutionally

)

(33,

K8 = (k21~) I12 ÷ ( 6 + 4 w 2 - 7 ~ ) i 1 2

important

for matrix oxides with het-

because often heterovalent ions are dissolved substi-

into the matrix

lattice.

Then,

equivalent amount of defects is created increasing point defect concentration,

for each h e t e r o v a l e n t

ion an

Jl

(e.g. Ti4~i and VNi in NiO). With the diffusion

ated and often Di is found to be proportional

is normally acceler-

to c i over a range of con-

centrations c i . The general

case

in which the chemical

composition

cannot

be handled

diffusion

analytically.

Here,

coefficients numerical

vary with

methods

must

be used to solve the system of transport differential equations. With

increasing

overlap

diffusion

eventually.

time,

the

concentration

If the Gibbs f o r m a t i o n

strongly negative,

the product

solubility

at very low concentrations

product

growth of the AB-precipitates cleation supersaturation, dinate

of the activities

follows.

profiles

of A and B

energy of the compound AB is of A and B reaches

the

of A and B. Nucleation

and

If one neglects the effects of nu-

the product AB forms inside the matrix at coor-

~* at time t*, when the product of the activities of the reactants

aA'a B exceeds the solubility product

a A • a B = L(max)

(34)

The solubility product is given by the Gibbs energy for the chemical reaction

A(Y)+_B(~)

=

AB ;

&G

=

AG~(AB)-( AG(A(~[))+ dG(B(~))

(35)

In~m~ Reactions

where

dG

is the Gibbs

energy

of the

43

chemical

Gibbs energy of formation for AB and ~G(~(~)) energies of solution of A and B in ~. strain

energies

matrix,

become

important

reaction,

and

dG~(AB)

~G(B(~))

is the

are the Gibbs

If interracial energies and elastic

for the initial

formation

of AB in the

corresponding terms have to be introduced in the energy balance of

the AB-formation.

As a consequence,

From these conditions, culated.

the precipitation would be retarted.

the location of the first precipitation can be cal-

Numerical results were presented in [69] for the following cases:

i) 5 A and 5 B are constant, and 4) D A C C A

2) DA ~ c A and D B ~ C B , 3) D A N c A and D B = const,

and 5 B = D~ + D°-CA,

by d i s s o l v e d

A.

The

calculations

i.e. the diffusion of B is accelerated show

that this

type

of

internal

state reactions occurs only under special kinetic conditions.

solid

In case

(i),

the ratio of the chemical diffusion coefficients of A and B in the matrix must not e x c e e d a value interfaces of matrix comes an

'external'

5 to i0. Otherwise,

~(C) one.

precipitation

occurs at the

and the reactants A or B, and the reaction beThe locus of the first p r e c i p i t a t i o n

determined by the ratio of the chemical diffusion coefficients; mum)

solubilities

persaturation

in the matrix play only a minor role.

is necessary

zone of precipitates of the chemical N

for the AB-formation,

forms,

diffusion

coefficients.

the precipitates

(maxi-

If a certain

su-

a more or less extended

which depends on the concentration In the cases

CB, precipitation occurs essentially at

is mainly the

of DA ~

dependence c A and DB

~*. If DA and 5 B are constant,

form in an extended region around

~*.

After AB-nuclei have been formed, they grow in the perturbed flux field of A and B, which diffuse further into the interior of ~he matrix ~. The precipitate

morphology

the anisotropy

which

tions of the precipitate, gies.

Elastic

energy

large

volume

served

now depends

on the growth kinetics,

changes.

bands

and on the precipitate/matrix

terms become

phase ~ varies w i t h c A nucleation

evolves

on

of the matrix ~ which dictates the preferred growth direc-

and

important,

if the

(cB) , or if the p r e c i p i t a t i o n During the

the g r o w t h subsequent

of the

interracial

ener-

lattice constant process

initial

precipitate

results

nuclei,

of in

further

growth have been ob-

[68,70].

At an advanced agglomerate

stage of the reaction,

the

individual

to form a more or less continuous

dispersed precipitate particles. the s o l u b i l i t i e s

AB layer,

The final morphology

of A and B in the matrix,

precipitates

the

either

or they grow as

strongly depends

solubility

product,

transport properties of the matrix and the precipitate phases,

on the

and on in-

terracial energies.

The morphological ticle

evolution of an assumed single spherical AB

in the perturbed

diffusion

field of the matrix has been considered

in [69]

for short time

cussed,

i) The isolating precipitate

ing precipitate

increments.

(D prec >> D ~)

(small) par-

Three d i f f e r e n t

cases have been dis-

(Dprec << D~),

2) the short-circuit-

and 3) short-circuiting

by the precipitate

44

H. Schmalzri~ ~ d M. Backhaus-Ricoult

interfaces. tivity

In the two latter cases the precipitate

surface,

A(B)-diffusion

which causes a symmetrical direction,

interface

precipitate

is an isoac-

growth

even if D ~ + D~. The precipitate

in the main

grows preferen-

tially in this main diffusion direction and slower perpendicular to it. Therefore, formation of rod-like precipitates in the diffusion direction is expected. In the case of a low-conducting interface trations ments

precipitate

is no longer an isoactivity

(DPrec~<

D ~) the precipitate

surface.

This means that the concen-

vary with the locus on the interface.

For very small time incre-

and DA/D B + 1, preferred

rection is now observed. coefficients

(Di/~),

growth perpendicular

to the diffusion

di-

For an increasing ratio of the chemical diffusion

the precipitates

become more

and more asymmetric.

The preferred growth is towards the side of the slower diffusing reactant. For large

ratios

(D~/D~),

the precipitate

centre

is displaced

considera-

bly. Mathematical precipitate

difficulties geometry

viour of the single tates.

However,

tinuous

boundaries

did not allow consideration precipitate,

long-time

an ensemble

The morphological

very slow transport

in the AB-product

has been assumed.

In almost

phase

(or agglomerated

beha-

where a con-

stability of the

Again a very fast or

a

(relative to the matrix trans-

all realistic

faces were unstable against fluctuations

in

of precipi-

the final stage of the reaction was studied,

of this AB-layer has been investigated.

nar interfaces

and the change

of the

not to mention

layer of AB should have formed.

interfaces port)

due to the moving

cases,

the planar

inter-

in form. This means that non-pla-

precipitates)

are expected

to represent

the final morphology.

Experimental Extensive

observations

experiments

tions with A = CaO, liminary CoO,

experiments

(liquid)

vestigate however,

were done on internal ~(~) + ~(~) = AB-type of reacB = TiO2,

C = NiO and AB = CaTiO 3 (perovskite).

are available

with various

CaO-A1203-silicate,

the AB-phase

formation

other matrices

and even oxide as a surface

we shall report only on the internal

surfaces

reaction. perovskite

Pre-

C, such as

(A1203)

In this

to insection,

formation

in the

NiO-matrix. The system diagram

CaO-TiO2-NiO

of Fig.

The solubility tion,

21,

Dca(NiO)

=

in its essential

internal

reactions

features

at T = 1375°C.

and temperature

The chemical

to the phase

can be expected

of CaO and TiO 2 in NiO are 0.06 and 0.014,

respectively,

this composition

conforms

so that

diffusion

to occur.

in mole

frac-

coefficients

at

have also been determined:

7.3.10 -11 cm2/s; DTi(NiO)

= 6.9.10 -10 cm2/s

(unpublished work).

Internal Reactions

45

C

A Fig. 21.

AB

B

Gibbs phase diagram A-B-C for a possible internal re-

action (A+B=AB) -system.

Fig.

22 shows the p e r o v s k i t e b a n d t h a t was p r e c i p i t a t e d d u r i n g the

inter-

hal r e a c t i o n CaO + TiO 2 = C a T i O 3. In a c c o r d a n c e w i t h the formal c o n s i d e r a tions,

[69],

its

location

was

found

close

v i e w of the fact that D c a / ~ T i ~ 0.i. Often,

to t h e

CaO/NiO-interface,

in

a d d i t i o n a l p r e c i p i t a t i o n bands

f o r m e d a f t e r the f o r m a t i o n of the first one. The p r e c i p i t a t e p a r t i c l e s had the

perovskite

structure

lets w e r e twinned,

and g r e w

essentially

as platelets.

These

plate-

but the t w i n n i n g may h a v e o c c u r r e d d u r i n g cooling.

Fig. 22. CaTiO3-precipitate band in NiO at 1340°C, in air, t = 413 hrs.

46

H. Schrnalzfied and M. Backhaus-Ricoult

Additional

experiments

presaturated the

CaTiO3-reaction

contacted

have been made with NiO-matrix

with C a O ( 1 % ) front

at the surface

could be observed. the p e r o v s k i t e

and T i O 2 ( 1 % ) .

grew parabolically

In the case of TiO2-doped

grew mainly

near

the

Finally,

an initial

trix crystals, stage

of the

internal

by diffusing one obtains

dense

replacing

became

diffraction

structure. (e.g.

for ABO 3 compounds,

ion sublattice, and

O2--ions

in

order

to

which

form

which

is

the internal

ilmenite

is almost

of

at the side

section. precipitate

dense-packed

perovskite

In this way stability

This was expected

structure).

the rearrangement

the

two NiO-ma-

was continued

One may have anticipated

in the

would have avoided

unstable.

in the previous

show that

forms with the perovskite form first

reaction

sides of NiO.

layer. The caTiO3/NiO-interface

able products structure

internal

morphologically

patterns

CaO,

band at an advanced

about the morphological

because CTi'DTi > Cca.Dca , as discussed Electron

contacting

between

precipitation

Then the

information

a dense internal precipitation

phenomenon

CaO/NiO(TiO2)-interface,

CaO and TiO 2 from the two opposite

of the TiO2-reactant

after

layer of CaTiO 3 was plac~d

experimental

if it was

No Liesegang

NiO,

NiO,

in the matrix.

the perovskite

reaction.

which were

into the matrix

with NiTiO 3 at 1385°C.

again due to the higher Ti-mobility

crystals

In the case of CaO-doped

CaTiO 3

that metastThe

ilmenite

in its oxygen

of the large

from

the

Ca 2+-

dense-packed

fcc-NiO-matrix. INTERNAL REACTIONS

DRIVEN BY OTHER THAN CHEMICAL POTENTIAL GRADIENTS

In the previous

sections,

we discussed

duced by chemical potential necessary concentrations front, ents.

systems,

where

reactions of the

potential

One then expects

ditions. In this section

analyze

the driving

individual

electric

gradi-

under appropriate which

with

in ionic

field strength.

V Jd # 0, i.e. fluxes

occur

con-

Those

if the divergence

(jd) does not vanish.

inhomogeneous

This

systems,

where

A/AX/AY/A,

under

are spatially variable.

in heteroDhase

of mixed

fluxes

potential

assemblaaes

ionic/electronic

conductors,

e.g.

load, can serve to exemplify the general problem of this section.

Let us assume in order

if

that we are dealing

Internal reactions

reactions

is the electrical

ionic and electronic

means

to occur,

internal

force

to induce

other than chemical

to take place

the transport coefficients

Assemblages

gradients

in-

at the internal reaction

It is of course possible

similar reactions

we will

are expected

necessarily

formed.

fluxes which were

When the point defects attained the

(~ component activities)

new phases were

by thermodynamic

point defect

gradients.

that the anionic

to simplify

are disregarded.

transference

the argument.

For the transference

Also,

number

interface

is vanishingly polarization

numbers we then have

small, effects

Internal Reactions

tA(AX)+te(AX )

=

If I = I i + I e ,

i ;

tA(AY)+te(AY )

=

47

1 ;

tA(AX)

~

tA(AY)

(36)

~ I = O, and t h e r e f o r e we can w r i t e

IA(AX ) + I e ( A X )

=

IA(AY ) + Ie(AY )

(37)

F r o m t h e s e e q u a t i o n s we can d e r i v e

aI A

=

IA(AX)-IA(AY )

w h i c h m e a n s t h a t if

= &IA(AY ) • ~ t A / t A ( A Y )

---

~tA.I

(38)

A t A + 0, the c a t i o n i c flux is c h a n g i n g its d e n s i t y at

the A X / A y - i n t e r f a c e .

In o t h e r words,

the

interface

is a c t i n g

either

s i n k or as a s o u r c e for A, w h i c h d e p e n d s on the A + - f l u x direction, ed t h a t a s u f f i c i e n t l y the d i f f e r e n c e

high electric

field

is applied.

Since

as a

provid-

nt A = ~te,

in the e l e c t r o n i c c u r r e n t b e t w e e n the two p h a s e s AX and A¥

p r o v i d e s the n e c e s s a r y e l e c t r o n s for the r e d u c t i o n of the A - c a t i o n s or the oxidation have

all

terface

of the the

anionic

features

operates

species.

of an

These

processes

(electrochemical)

as an A-source,

at the A X / A Y - i n t e r f a c e

internal

if lattice m o l e c u l e s

reaction. AX

(or A¥)

The

in-

are de-

c o m p o s e d in the f o l l o w i n g way

A X = 1/2 X 2 + -~ A + + ~e~

;

A¥ = 1/2 ¥2 + A+ + e' --~

In a s t r i c t sense, A should small

already

applied

the d e c o m p o s i t i o n

(eq.

(39))

AX a n d AY) newphase.

voltages.

However,

in p r a c t i c e

has to be b u i l t up to o v e r c o m e Fig.

force,

a certain

i.e.

at very

A-supersaturatlon

= A, w i t h ~A+ - c o n s t a n t in

the n u c l e a t i o n

barrier

23 g i v e s a s c h e m a t i c r e p r e s e n t a t i o n of the situation.

AX

AY

A+

A+

e'

e'

A'+e'

Fig. 23. Transport processes (schematic) . ,,tF'SSC 22:1-0

or the f o r m a t i o n of m e t a l

take place with a vanishing driving

(= e l e c t r o n s u p e r s a t u r a t i o n in v i e w of A + + ~

(39)

4--

:

Am

in the galvanic cell A/AX/AY/A

of the

48

H. $clm~lzried and M. Bacldmus-Ricoult

In all the cases, the a m o u n t method

the crystal

of d e c o m p o s e d

AX(A¥)

for the measurement

transference

matrix

at this

of extremely

By a determination

interface

one has

small changes

of

a sensitive

in the electronic

number of ionic crystals.

Internal reactions

in systems with varvinu disorder tvDes

In the p r e v i o u s

section,

state reactions.

We now discuss

ternal

is destroyed.

reactions

we i n t r o d u c e d

in inhomogeneous

From the foregoing,

in general

electrochemical

the general

case of

crystals

internal

internal

with varying

reactions

solid

(electrochemical) disorder

occur

in-

types.

if in a crystal

matrix the condition V J i o n = 0 is not met. The extreme is a transition from electronic (n or p) conduction to ionic conduction inside a crystal, which we name a (n-i)-junction. Since atomic

defects

thermodynamic) ductor

in ionic crystals

relationships

(p-n)-junctions,

tive description

These

obey Boltzmann

statistics)

equation

the d e f i n i t i o n

of the e l e c t r o c h e m i c a l

Electrochemical predetermined which

section,

and

potential

reactions

occur

by externally

= ~i + ~i'

which means that ~i By this

to the deviation

linear

their phases

but some

practical

if ionic crystals gradients

voltages.

transference

One then expects

in the predetermined

number

spatially.

are brought

nipulation since

relevance.

~I

into the

observations These

gradients

became

or if they change

Electrical

are available permit

to

in the previous

current-in-

the

which

placement

zone without

exten-

emphasize of new

any chemical

ma-

from outside the crystal. = O, a change

from electronic

cessity an electrochemical

reaction

way as the other types of internal transport,

reactions

(n-i)-transition

in

simultaneously,

to those described

in part electronlc conducting,

interesting

(in-situ)

ap-

from the equi-

duced internal solid state reactions have not yet been investigated sively,

i = sys-

is the rate of produc-

junction.

applied

that the crystal

(electronic)

needed

potential

are analogous

in part ionic conducting, their

-

(~i

thermodynamics,

in the

and electrical

which

provided

and holes the

=

(relaxation process).

internal

phenomena

(Ji

inter-

~ is the net charge density)

the final equation of defects

chemical

can be induced

observe

electrochemical

cibi" V ~ i ) '

this rate is directly proportional

librium concentration

and

in semicon-

that one is dealing with non-equilibrium

of irreversible

(or a n n i h i l a t i o n )

proach,

(kinetic

(as long as electrons

( A ~ = I/E.~ o- ~ , where

is locally well defined,

i.e.

are the flux equations

zi.F. ~ ). By the assumption

tion

(n-i)-junctions,

basic relationships

tems in the framework

counterparts

the same set of equations are used for a quantita-

of internal

hal reactions. Poisson

obey the same formal

as their electronic

defect

the precipitate

relaxation

morphology).

to ionic defect

inside the crystal, reactions,

and nucleation Since

fluxes

which,

is governed

and growth

all these processes

is by ne-

in the same

kinetically

by

(the evolution

of

take place

in the

~m~R~cfi~s

interior

of the host crystal,

the matrix

and

elastic

in the precipitates

49

and plastic d e f o r m a t i o n

as well.

occurs

These deformations

the reaction kinetics and in particular the growth morphology. see an essential difference to the electronic phenomena

in

influence

Here we can

in semiconductors:

whereas in these purely ionic processes the site balance of the host crystal lattice is not affected, ternal

the electrical

in in-

(n-i)-junctions destroy the crystalline matrix.

Electronic defects

in ionic compounds result in compound nonstoichiometry.

Since their mobility

is much

defects,

(n-i)-junctions

one expects

larger than the mobility

high intrinsic ionic disorder been h e a v i l y

doped

(e.g.

compounds,

i.e.

make the normally

(e.g. AgBr),

Experimentally,

produce

position).

or in ionic crystals which have

By inducing very high or very

low

one can thus inject electronic defects into a small

nonstoichiometry

and

in this

way

ionic conductors semiconducting.

galvanic

double cells

chemical potential gradient the electrical

of the ionic point

to occur in compound crystals with a

ZrO2(+CaO)).

chemical component potentials, these

field driven reactions

field

can be used to e s t a b l i s h

(in order to produce the

both the

(n-i)-transition)

and

(in order to induce a current and the internal decom-

A cell of this kind is schematically shown in Fig. 24.

I #!

!

PO2

AU

\

AOn >>

A

I!

BO

AOn >> A

02(g)

>

,I

U1 Pig.

24.

tential

U2

Galvanic double cell for the build-up of chemical p o gradients in BO. AO is a solid electrolyte.

For our further discussion, Wagner

AgBr may serve as an example.

[72] showed that if a (low) voltage

cell Pt/AgBr/Ag, near the anode

Hebb

[71] and

is applied to the polarization

one may have a change in transference number from t h = 1 (Pt) to tAg = 1 near the cathode

(Ag). But at sufficiently

low applied voltages dU, one does not observe any internal decomposition. The silver the anode very small

ion current

is suppressed,

to the cathode. electronic

In this way

conduction

and only e l e c t r o n holes it was p o s s i b l e

in ionic

crystals.

at the anode of the steady state polarization cell is

The

flow from

to d e t e r m i n e

the

silver potential

50

H. Schmalzriodand M. Backhaus-Ricoult

"Ag

=

,~g -

and consequently

~Br

=

The theory

~U

• F

one has for the bromine potential

"~r +

~U

~U

of the polarization

is increased

mine potentlals anode

(40 b)

• F

found in the literature If

(40 a)

cell

is thoroughly

worked

and the system is closed at the anode,

( electron

hole

in the AgBr-crystal.

The

concentrations) supersaturated

react with the AgOg-structural

The arrows

=

indicate

bromine

process

electron

into atomic

[Br]

lattice molecule ening,

' + h" + (VAg

Br~r ) + A=~g~

that carry the

of the structural

element

filled with a bromine activity

near the

which

(41)

[Br] + A=.gg,~

=

(positive)

elements

of the crystal,

atom.

Eq.

in the

have

region of AgBr, can

electrical

in the bracket

but the smallest

(41) describes

(n-i)-junction

holes are transformed and outgoing

Ag~.

the

during the internal

If the neutral

sites form clusters,

where

bromine

and eventually

this is

possible

the electrochemical

zone,

cur-

is a (neu-

atom on the vacant site of a lattice molecule AgBr;

not a structural nal reaction

holes,

elements according to

the species

rent. The combination tral)

very high bro-

are established electron

been swept by the electric field into this near-anode

Br~r + AgOg + h"

out and can be

[72].

pore inter-

incoming

high

decomposition atoms on empty

perform Ostwald

rip-

they should become a visible cloud.

The reaction

(41)

is composed

of two parts:

1) the Frenkel

defect

forma-

tion reaction

(42)

and 2) the formation of neutral Br-atoms according to

Br~r + V~g + h"

=

[Br]

(43)

InternalReactions In view of the many structural

elements

51

involved in the overall reaction,

a number of serial reaction steps may govern the reaction kinetics of this internal

decomposition.

If the steps

involvlng

fast ones

(since D h >> Di), the rate of the

reaction,

eq.

action

(42), becomes rate determining for the overall

Frenkel

internal re-

(41). This is true as long as Ag~ is responsible for the silver ion

transport. means

the electron hole are the

(locally homogeneous)

If,

that

in contrast,

these

(n-i)-junction

I VAg

vacancies

is responsible

start

for this transport,

which

at the cathode and sweep towards the

zone, the Frenkel defect formation process

in the internal decomposition reaction

is not involved

(i.e. the bromine formation process

occurs according to ~VAlg + -~ h" + Br~r = [Br]). In order to set up the kinetic equations reaction,

which

is not elaborated here

realize that the

(homogeneous)

for the electrochemical

in detail

Frenkel reaction

(see, however

is a bimolecular

which can be treated according to standard kinetics.

internal [73]),

we

reaction

It has to be coupled

with the flux equations of Ag~ and h'. The kinetic formation equation is

=

oz • (l-(k/k).(ci-cV/C°~))

=

(44)

so that the maximum formation rate is obviously

c(max)

=

~

• c °z

(45)

and thus the maximum flux density from the internal reaction zone

(satura-

tion flux)

j(max)

;

~!rl

-i.d

--

--> k-

c°

2,

if ~ ~R is the width of the internal reaction zone.

(46)

Since

~ R should scale .

with ~Di., R = ~Di.c°/~ , we expect j(max) to depend on the rate constant of the Frenkel formation reaction, silver interstitlal

J(max)

=

and on the transport coefficient of the

ions as

f(c O, ~ U)

~i.~

(47)

so that in principle one can determine the Frenkel reaction rate constant from the saturation current of the (n-i)-junction in AgBr.

52

H. Sclunalzrie,d and M. Bacidzaus-Ricoult

As has been mentioned chemical cloud

internal

formation

the decomposition ments

before,

reactions

see Fig.

have been reported

near the anode voltage

with AgBr always

region,

not many experimental at voltages

have been made

25. This

indicates

to date.

which

on electro-

Observations

are sufficiently

[74,75,76].

show heavy pitting

studies

However,

of the s%rface

on

above

the experi-

near the anodic

i) that Br-supersaturation

is indeed

Pt( )

I-)Ag

~rz(g ) Fig. 25. Surface pitting due to internal supersaturation of point defects in AgBr and schematic explanation. ~U(Ag,Pt)=12 Volt, 46 hrs at T = 200°C.

present

in AgBr

in the anodic

in the bulk is quickly

bulk region,

compensated

2) that the formation

by equilibration

of

with surface-AgBr

cording to

|

[AgBr]sur f + [Br]bulk

=

•

%Br2(g ) + [AgSr]bul k + [V~gVBr]sur f

(48)

[Br] ac-

Internal Reactions

which

is made p o s s i b l e

by A g - d i f f u s i o n

53

from the surface to the bulk and

leads immediately to the surface pit formation. the simultaneous

flow of Ag~ and h"

Inward Ag-diffusion

(counterflow)

means

for electroneutrality.

Both species are abundant in the anodic region. Several

further

available

observations

(unpublished work).

on

electrochemical

internal

reactions

The formation of cloudy precipitates

are

in the

bulk of Ag-halides near the anode has occasionally been observed if a sufficiently

high

Pt/AgBr/Ag). lized

voltage

was

applied

to

the

polarization

cell

(e.g.

Dark zones migrating from the cathode into the bulk of stabi-

zirconia were also seen if a sufficiently

to the polarization

high voltage was applied

cell Pt/ZrO2(+CaO)/Pt,O 2. Zirconia

is known to become

a p-type semiconductor at high enough oxygen potentials and a n-type semiconductor

at

low e n o u g h

internal decomposition

one expects

that

can take place with the zirconia polarization

oxygen

potentials.

Therefore,

cell

(in analogy to the case of AgBr), except that in this case the ionic cond u c t i o n is by a n i o n s (oxygen ions), and the i n t e r n a l r e a c t i o n p r o d u c t should be formed by reduction of the cations near the cathode. or structural

analysis

yet been made. chemical

internal

theoretical,

of the precipitates

Therefore,

the indications

reactions

are

still

in the darkened

zones has not

for the occurrence

rather

indirect.

A chemical of electro-

However,

from

a

systematic point of view they belong to the category of reac-

tions as treated in this article,

and the prospects

for their further ap-

plications are most promising.

Acknowledgement:

This review was prepared while the first author was guest

of

de

Laboratoire

Physique

des

Mat~riaux

Department of Theoretical Chemistry, Volkswagen-Stiftung

and Deutsche

CNRS,

Meudon

University of Oxford

Forschungsgemeinschaft

(France)

(UK).

and

Funding by

(SFB 173)

is very

much appreciated.

References

(I)

R.E. Liesegang,

(2)

C. Wagner,

J. Electrochem.

Soc.

(3)

C. Wagner,

Z. Elektrochem.

83, 772

(4)

F.N. Rhines and A.H. Grobe, Trans. Am. Inst. Min. 147, 318

(5)

Naturw. Wochschr.

11, 353

103, 572

(1896). (1956).

(1959). (Metal1.)

Engrs.

(1942).

J.L. Meijering and M.J. Druyvesteyn,

Philips Res. Rep. 2, 81 (1947).

H. Schma~d~ ~dM.B~klmu~¢o~t

(6) (7)

I. Dietrich and L. Koch,

F.N. Rhlnes and W.A. Johnson, 147, 205

Trans.

50, 31 (1959).

Am. Inst. Min.

(Metal1.)

Engrs

(1942).

(8)

H. Schenck et al., Arch.

(9)

W. Schwarzkopf,

(10)

Z. Metallkunde

EisenhQttenwesen

Z. Elektrochem.

31, 121

(1960).

53, 830 (1959).

E. Verfurth and R.A. Rapp, Trans.

Am. Inst. Min.

(Metal)

Engrs.

230,

1310 (1964). (11)

J.L. Meijering,

(12)

R.A. Rapp, Acta Met. g, 730

(13)

C. Wagner,

(14)

R.L. Klueh and W.W. Mullins,

Acta Met.

17, 69 (1969).

(15)

R.L. Klueh and W.W. Mullins,

Acta Met.

17, 59 (1969).

(16)

V.A. van Rooigen et al., Acta Met. 23, 987

(17)

F. Maak,

(18)

C. Wagner,

Corrosion

Science 8, 889

(19)

R.A. Rapp,

Corrosion

21, 382

(20)

D. Wegener et al., Rad. Eff. Letters 85, 13 (1984).

(21)

H. Schmalzried,

(22)

F. Schneider and H. Schmalzried,

(23)

T. Pfelffer and H. Schmalzrled,

(24)

K.M. Ostyn et al., J. Am. Ceram.

Soc. 67, 679

(25)

F. Schneider and H. Schmalzrled,

Z. Phys. Chem. NF 160, 19 (1990).

(26)

K.M. Ostyn et al., Beitr. (BEDO)

Z. Elektrochem.

(1959).

(1961).

J. Colloid Sci. 5, 85 (1950).

Z. Metallkunde

160,

63, 824

52, 545

(1975).

(1961). (1968).

(1965).

Bet. Bunsenges.

Phys. Chem. 87, 551

(1983).

Z. Phys. Chem. NF 166, 1 (1990). Z. Phys. Chem. NF 161, 1 (1989).

Elektronenmikroskop.

(1984).

Direktabb.

Oberfl.

19 (1990).

(27)

S.R. Summerfelt

and C.B. Carter,

(28)

C.B. Carter et al., J. Physique

Ultramicroscopy 47, (1988).

30, 150 (1989).

Internal Reactions

(29)

D. Ricoult and H. Schmalzried,

(30)

M. Schnehage et al., Ber. Bunsenges.

(31)

D. Ricoult and H. Schmalzried,

(32)

D. Ricoult,

(33)

W. Luecke and D.L. Kohlstedt,

(34)

F. Schneider,

55

J. Am. Ceram.

Soc. 70, 669 (1987).

Phys. Chem.

86, 1061

J. Mat. Sci. 22, 2257

(1982).

(1987).

unpublished results.

PhD-Thesis

J. Am. Ceram.

1987,

Soc. 71, 189

(1988).

Institute Physical Chemistry,

Univer

sity Hannover. (35)

K.D. Becket and S. Dreher,

Bet. Bunsenges.

Phys.

Chem. 93, 1382

(1989). (36)

K.D. Becket,

(37)

D. Ricoult and H. Schmalzried,

Solid State Ionics 39, 27 (1990). Bet. Bunsenges.

Phys. Chem.

90, 135

(1986).

(38)

B.P. Wirtz and M.E.

(39)

A.D.

(40)

B.P. Wirtz and M.E. Fine, J. Am. Ceram.

(41)

G.W. Groves and M.E. Fine, J. Appl. Phys. 35, 87 (1964).

(42)

H. Knoch and B. Reppich,

Science of Ceramics 9, 463

(43)

H. Knoch and B. Reppich,

Science of Ceramics 12, 537

(44)

T. Wu and D.L. Kohlstedt,

(45)

D.L. Kohlstedt and J.B. van der Sande, Contrib. Mineral.

Fine, J. Appl.

Inglis et al., J. Mat.

Phys. 38, 3729

Sci. 17, 2939

J. Am. Ceram.

(1967).

(1982).

Soc. 51, 402

Soc. 71, 540

(1968).

(1977). (1980). (1988). Petrol.

53,

13 (1975). (46)

D.L. Kohlstedt et al., Science 191, 1045

(47)

S. McKernan et al., Mat. Res. Soc. Symp. 447

(48)

C.B. Cook et al., Solids 120, 207

(49)

H. Schmalzried,

(5o)

H. Falke, Hannover.

Bet. Bunsenges.

PhD-Thesis

1987,

(1976). (1990).

(1990).

Phys. Chem. 88, 1186

(1984).

Institute Physical Chemistry,

University

H. Scimtalzncdand M. Backhaus-R~ult

56

(51)

M. Backhaus-Ricoult,

unpublished results.

(52)

H. Falke, Diplomarbeit 1982, Institute Physical Chemistry, University Hannover.

(53)

H.-J. Engell and H.K. Kohl, Z. Elektrochem.

(54)

N.L. Peterson and W.K. Chen, J. Phys. Chem. Solids 43, 29 (1982).

(55)

M. Backhaus-Ricoult and D. Ricoult, J. Mat. Sci. 23, 1309 (1988).

(56)

M. Backhaus-Ricoult and C.B. Carter, J. Am. Ceram. Soc. 70, C 291

66, 684 (1962).

(1987). (57)

D. Ricoult and H. Schmalzried, Phys. Chem. Min. 14, 238 (1987).

(58)

J. Narayan et al., Mat. Res. Symp. Proc. 24, 101 (1984).

(59)

J. Narayan et al., Phil. Mag. & 49, 287 (1984).

(60)

J. Narayan and ¥. Chen, Phil. Mag. A 49, 475 (1984).

(61)

M. Backhaue-Ricoult and S. Hagsge, Acta Met.

(62)

M. Backhaus-Ricoult,

(63)

C.B. Carter and L. Tietz, personal communication.

(64)

K.M. Ostyn, PhD-Thesls 1983, Dept. Mat. Sci. and Eng., Cornell Uni

(in print).

unpublished results.

versity. (65)

K. Merkle, Mat. Res. Soc. Symp. Proc. 122, 69 (1988).

(66)

W.H. Tuan and R.J. Brook, J. Europ. Ceram. Soc. 10, 31 (1990).

(67)

B. Reppich, H. Knoch, in "Deformation of ceramic materials", R.C. Bradt, R.E. Tressler, eds., Plenum, New York, 1983.

(68)

H. Schmalzried et al., Z. phys. Chem. NY 166, 115 (1990).

(69)

M. Backhaus-Ricoult et al., Ber. Bunsenges. Phys. Chem. 95, 1593 (1991).

(70)

T. Frick, PhD-Thesis 1992, Institute Physical Chemistry, University Hannover.

57

Internal Reactions

(71)

M.H. Hebb, J. Chem. Phys. 20, 185 (1952).

(72)

C. Wagner, Proc. C.I.T.C.E.

(73)

H. Schmalzried, Chemie, Weinheim

(74)

7, 361 (1955).

Kinetics of Chemical Processes in Solids, Verlag (in preparation).

Th. GroBe, PhD-Thesis 1990, Institute Physical Chemistry,

University

Hannover. (75)

U. Stilkenboehmer, Diplomarbeit 1991, Institute Physical Chemistry, University Hannover.

(76)

Th. GroBe and H. Schmalzried,

Z. phys. Chem. NF 172, 197 (1992).

Further literature R.L. Shook et al., Met. Trans. A 16, 1815 (1985) C.A. Handwerker et al., in: Metal and Ceramic Matrix Composites, R.B. Bhagat et al., eds., TMS publishers 1990, p. 457.