Crystal chemistry of magnetic oxides part 1: General problems — Spinels

Crystal chemistry of magnetic oxides part 1: General problems — Spinels

Prog. Crystal Growthand Charact 1984, VoL 9, pp. 263-323 0146-3535/84 $0.00 + .50 Copyright ~ 1984, Pergamon Press Ltd. Printed in Great Britain. A...

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Prog. Crystal Growthand Charact 1984, VoL

9, pp. 263-323

0146-3535/84 $0.00 + .50 Copyright ~ 1984, Pergamon Press Ltd.

Printed in Great Britain. All rights reserved.

CRYSTAL CHEMISTRY OF MAGNETIC OXIDES PART 1' GENERAL PROBLEMS SPINELS -

-

E. Pollert Institute of Physics, Czechoslovak Academy of Sciences, 180 40 Prague 8 - - Libe5, Na Slovance 2, Czechoslovakia (Received 4th A p r i l 1984)

ABSTRACT

Most

of the m i x e d

of g a r n e t s , by

close

packed

the

suitable

are

introduced.

damental ty a n d

oxygen

size,

of the

oxides

are

of the

centrated

on s p i n e l s ,

between

the

and

of the

and

ehiometry

and

is d i s c u s s e d

to the the

last

by

the

magne-

of v i e w part

of v a r i o u s

in

is

on

of c a t i o n s

position,

mac-

of c l u s t e r s

of

the

con-

cations

formation

the

General

mixed

second

Destabilization

of

two f u n -

minimum.

point

from

of

configuration

distribution

deviations

formed

electroneutrali-

oetahedral

influence

in the

of

The

distortion,

of c a t i o n s .

due

the

this

exception

cations

is d r i v e n of

influence the

which

energy

from

the

sublattice

electron

article.

tetrahedral

ordering

Gibbs

namely

Jahn-Teller

structure

and

chemistry

discussed

properties,

into

formation

crystal

part

rosoopio

anions

with

the

condition

the f i r s t

their

from

valency

Their

condition

oxides,

derived

conditions,

problems tic

magnetic

c a n be

the

ideal

spinel stoi-

cation

properties

a long

time period

part.

i. I N T R O D U C T I O N

Magnetic basic with

oxides

are materials

properties regard

their useful

to

research

as w e l l the

contemporary

are not

to a t t e m p t

at

studied

as w i d e

by f a r

least

already

field

of the

evolution exhausted.

partially

one From

applications. can

to e x p l a i n

263

say

that

this reason

for

their

Nevertheless possibilities it

the r e l a t i o n

seems

of

to be

between

their

264

E. Pollert

structure

The

and properties.

semi-covalent

suggests ion

as

that metallic

compounds

is22s22p 6 and mostly

situation

of a l l

this

different

valency

by

a eomplex and

oovaleney.

tions

and

give

rise

of

individual

ions.

turally

anions

the

not

occupied the

antiparalel

that

The

described and

nificantly

of v i e w

The

that as

the

the

atoms of

of i o n s can

ions

cations

forces

These

electron to :~ s t a b l e

with

paired

of

others

earths magnetic

the h i g h

of l o c a -

the

degree

crystal.

coexistence

the

are placed and

among

At of

the

same

ions with

two

~re

are

by

or m o r e

is

element

the

Pauli's

moments

of

same

sublattioes one

Let

two strucions with

are

and ma6ne-

sublattiee

is

compensation

us n o t e

different

the

~ntiparallel.

to e o m p e n s a t i o n

least

with

their posi-

in which the

by

field

the m a 6 ~ e t i c

is

incomplete

and ferrimaGnetism. same

with

ordering

leads

or at

The result

~nd

of m a g n e t i c

occupied

two

split

materials

which

affeeted

crystal

determine

the basic

only~

are

the

combined

whieh

eases:

in a n e n v i r o n m e n t

they

ions,

states forces

in which

ions.

of

finally

valeney

in

to f e r r o m a ~ n e t i s m .

oxides 9 particularly

range

of

properties

that

and rare

in nonvanishin~

is

orientation

oxides

sublattices

lead

the

other

the moment

of

in

these

mutual

moments

indicates

best

behaviour

erystallographically

of c r y s t a l as b y

anions~

metals

result

interactions

materials

kinds

their

transition

electronic

of m a g n e t i c

discussion

lattice.

of

and

e.,

lattice.

of a w i d e

This

as w e l l

such

existence

point tion

for

character

also

of

~enerally

to d i s t i n g u i s h

circumstances

electrons

oxygen

magnetic

magnetic

the presence

certain

the

to a n a b i l i t y

ma~netie

several

of

are modified.

equivalent

by

that

i.

approximat-

configuration

the valence

cations,

can

as w e l l

orystal~

antiferroma~netism

of

the

electrostatic

orientations

Loss

eontribution~

in first

electron

of

in ions

crystal

In most

equivalent

least

02- with

cations.

to

to e x c h a n g e

is n e c e s s a r y

different

tic but

of

at

ionic

shell

at p a r t i e u l a r

Consequently

properties

it

in the

occupations

principle

Then

exists

results

influence

prevailing

moment.

to a p p r e c i a t e

oxygen

anions

metal

condition

tendency

with

be regarded

outer

electrons

is n e c e s s a r y

formed

may

oxygen

d or f s h e l l s

A principal

lization

It

ma~letic

incomplete

time,

by

in a filled

zero

A different

moment.

oxides

formed

oor~figuration similar

and

where

of b o n d s ,

corresponding

results

electron spins

character

eleotronie

like

the properties

chemistry

the

distribution

known

structural

are

electrical

types

are

and

of m a ~ e t i e

determined

of G i v e n

localization

states

by

cations listed

in with

the

sig-

optieal.

oxides

their

of

ir~luence

from

chemical specific

some

baste

the

composicrystal data

Crystal chemistry of magnetic oxides

in Table

This

265

I.

first

materials

part with

perovskites

of our c o n t r i b u t i o n spinel

structure.

and h e x a g o n a l

Table

Structural

The

ferrites

I. P r i n c i p a l

second

will

formula

to some

part

where

general we

problems

shall

and

deal with

be p u b l i s h e d .

structural

General

type

is d e v o t e d

types

of m a g n e t i c

oxides

Number

Coordination

of c a t i o n

numbers

sublattiees

cation

of

Magnetic structure

sublattioes 6

A F , F , F i x)

2

6,12

AF,F,WF

2

4,6

Fi,F,AF

MMeI2019

5

4,5,6

Fi

ilmenite

MeMeO 3

1

6

W F , A F , F i x)

garnet

M3MesO12

3

4,6,8

Fi,AF

NaCI

Me0

i

perovskite

MMe03

spinel

MeMe204

magnetoplumbite

M - large

cations

8-fold Me

and

- small

substituted

12-fold

cations

4-fold

and

into

the sites

with

ooordination~

substituted

6-fold

into

the

sites w i t h

coordination,

F - ferromagnetism, Fi - f e r r i m a g n e t i s m , Fi x) - s e c o n d a r y

ferrimagnetism,

AF - antiferromagnetism, WF - w e a k

ferromagnetism.

2. G E N E R A L

Common tion

basis

of the

of garnets,

it is known, ABCABC

given

by

is

to the f a c e

the m a n n e r

there

exist

coordination

three

holes

with

formed

centered

cubic

(Fig.

cations

possibilities:

coordination by c a t i o n s

of their

oxides,

lattice

occupation

into

oxygen

(Fig.

l) a n d

the o x y g e n

ions,

of the n e i g h b o u r i n g in t w e l v e - f o l d

the

holes

oxygen

coordination.

As

type

type A B A B

lattice

occupation

excep-

anions. exist

structure

of t e t r a h e d r a l

oxygen

with

arrangement

2). T h e r e s u l t i n g

enter

of the n e i g h b o u r i n g

anions

AND STABILITY

by c l o s e p a c k e d

possibilities

lattice

in w h i c h

six-fold

of o x y g e n

OF F O R M A T I O N

of the m i x e d m a g n e t i c

the s u b l a t t i o e

to the h e x a g o n a l

-fold

ing

structures

two f u n d a m e n t a l

leading

leading

CONDITIONS

is

then

for w h i c h

with

four-

of o o t a h e d r a l

ions

and replac-

266

E. Pollert

Oc

@@ O

O

©

d Fig.

i.

Close-packed type

structure

ABCABC

and

face

0-<

Fic;.

2.

Close

To

derive

from their

the

spinel~ oxygen

perovskite lattice

properties~

and

into

namely

size~

Fundamental

eonditions

-

condition

of

the

eleotroneutrality

eondition

of

the

Gibbs

-

driving

ener~

cations

valency

the

and

formation

minimum.

of

the

l~tLiee.

!

of

hexaL~onal

hexa£;onal

which

spheres cubic

-0

structure and

the

eentered

:

packed

type ABABAB

of

the

spheres

of

[he

l~ttieeo

i'errite are

struotu~'es

substituted

electron

of

the

o~le with

e~n

st~ll'l

re~%ard

ea~rfi{~ura~ion.

~iven

struet1~e

are

to

Crystal chemistry of magnetic oxides

2.1.

Condition

of

With

regard

a possible

rious

to

valenoies

struotural

type and

anions

Generally the

it

electroneutrality

the

gen

is the

presenoe

important to

of

oations

oondition

simultaneously

for

keep

is p o s s i b l e

to

express

the

orystal

existenoe

given

ratio

lattlee

MI,

oxygen, tions,

M 2 are

Me a,

...

valenoies

of

for

large

small b,

-.,

a speoifio

of

cations

to

oxy-

oxide

of

an

arbitrary

type

by

cations

...

cations,

individual

~ ....

0z

substituted

entering

, b"

#

(Mel)a,'(Me2)

oations a

into

into

the

stoiehiometr±o

types

we

the

oxygen

tetrahedral ooeffioients,

z - stoiehiometrio

struotural

ean

ooeffieient

and

sublattioe

for

ootahedral

posi-

~ , ~ of

...

(i)

a = b =

,,,

=

a'+

o,.

= 3

C2)

= 4

(3)

b'+

a'#~'+

b'l~'+

0

...

=

(

8

=

(4)

2z)

- per ovskit e

a

+ b + .,.

a'+

b'+

,,,,

z

a.~

magnet oplumbit

a

+ b.~

+

(5)

= 1

(6)

=

(7)

..,

+ a

"~'+

b'~'+

....

6

( = 2~)

(8)

es

+ b + ...

a'+

= 1

3

b'+

.,,

= 1

= 12

~l , ~e ...

oxygen.

write:

spinels

z

-

in va-

of

formula

where

-

the

a mixed

M s

...

in the

eleetroneutrality.

(M1C(M2) ~

Then

267

(9)

(io)

268

E. P o l l e r

z

(il)

b./~+

a.¢,+ Basic

i9

=

cation valency

...

+ a'~,'+

combinations

%es f r o m w h i c h by f o r m a l dividual

structural

b',~'+

38

in spinels~

substitutions

types

....

( :

perovskites

series

types

of spinels~

(12)

and m a g n e t o p l u m b i -

of s o l i d solutions

can be f o r m e d are s u m m a r i z e d

T a b l e IX. B a s i c

2~)

in the in-

in the [Fable IX.

perovskites

and mag~-

netoplumbites

Structure

Typ

Spinel

0-3

Example -Fe203

1-3 2-3

perovskite

magnetoplumbite

Condition

2.2.

The

stability

crystal is

of

an

by

the

G

U is

the

in

at

H -

4-2

TiFe204

2-5

C o7/3Sb2/30!~

6-i

MoA~204

0-6

ReO 3

1-5

KNbO 3

2-4

CaTiO 3

3-3

LaCrO 3

2-3

BaFel2019

1-3-4

KFellMnOl9

3-3-2

LaFel2019

2-2-4

BaMg6Ti6019

a particular

given

general

=

Lio.sFe2.504 ZnFe204

(hypothetical)

energy m i n i m u m

ion

respectively

given

where

of Gibbs

3+ ["1 1/304) (Fe8/3

site

external

thermodynamic

TS

=

internal

condition

U + PV

crystal

-

contribution.

The effort

to m i n i m i z e

of c a t i o n s

into the o x y g e n s u b l a t t i e e

the

erystal

lattice

temperature of

the

Gibbs

and energqy

and

minimum.

413)

PV c o n t r i b u t i o n

energy

a

pressure

TS

energ2¢~

TS e n t r o p y

the Gibbs

in

conditions~

is d e t e r m i n i n g

and leads

of

volume

changes

and

for the s u b s t i t u t i o n

simultaneously

to f u r t h e r

Crystal chemistry of magnetic oxides

effects

from

distortions

2.2.3.

which

energy

crystal

character

have

ting

tual

EC~

Born

changes

i n the

Coulomb

distribution

energy

results of

with

all for

is

the

- preference

given

by

bond

where

high

and

with

energy higher

has

structural

are

the

field

cations

and

long range

stabilization

are

ideal the

repulsfrom

to a p p r o x i m a t e l y

In

repulsion

ions

oases, B i 3+

- Pb 2+, character It

the 10%

for

some

of

the

is d i f f i c u l t

influencing

Coulomb

energy

by

ener-

the

de-

consequences: with

compensated

higher

coordinat-

by s u r r o u n d i n g

in order

the r a t i o

for

the B o r n

ionic

to s i t e s

equivalent

in most

for

delooalized

sites

anions

to a c h i e v e

of c a t i o n s

result,

and

the

anions

oQvalen~2y.

and

fully

sublattice)

range

but

difference

generally

lowering

with

(one

to s h o r t

a sufficient

and

and

compounds

cases

may

superstructure

energy

electrons

on the

present,

on the

of the

having

as f o l l o w s

effects.

sublattice

for

mu-

type

when

of d i f f e r e n t

ordering

cations

inter-

Their

be c o n s i d e r e d

the f o l l o v i n g

valency

as

number

the

phenomena

oxygen

among

quantum

as B o r n

ions

s 2 a n d p6.

polarization

as w e l l

by

and

must

- Mo 6+,

of b o t h

to the

cases.

amounts

bond

principal valency

Eel represendue

= 0. D e t e r m i n i n g

gases,

o n the

bond

semicrystal

oovalency.

inasmuch

and

of the

and/or

and

formed

Eel

energy

ions

neighbourhood

of c a t i o n s

existence

having

internal

contribution

bond

term

is b e t t e r

ratio

the

type

higher

with

to o r d e r i n g

Crystal

ionic

the

charge

table

ing for

lattice

(14)

individual

their

of c a t i o n s

2.2.5.

with

Coulomb

kinds

the

the

of p r e s e n t

halogenides

of e l e c t r o n s

where

the

of the n o b l e

of the

the

to

stabilization

in

contributions

distances

tendency

charges

the

of the m a t e r i a l s

E B and

electrons field

This

shells.

- distribution

case

the O o u l o m b

electron

ion number,

maximum

in

Ebond )

the n e a r e s t

alkaline

of c a t i o n s

-

purely

by c o v a l e n c y

sharing of

(

charge

is

/i/.

cations

the

Minimalization

-

with

cations

to d i s t i n g u i s h gy by

bond

energy

effeoted

formation

With

configuration

(6 s 2) a n d f o r bond

crystal

influences

Coulomb

electron

above

of c a t i o n s

contributions

energy

outer

of the

of the

only

our

=

repulsion the

energy.

obtained

the

In

three

c a n be v a r i o u s

spheric

energy

of

orystal~

2.2.4.

ion

ordering

considered

contributions

total

with

ener~o~.

= E C + EB + E e l

energy

energy

actions

deal

of the b o n d ,

to be

U Coulomb

shall

of s t r u c t u r e .

Internal

covalent

we

269

of the

E C + E B ,v

O.

of

several a sui-

their

connected total

Contribution ooTalemt

at

with

symmetry.

Eel

character

is d e c i d of

the

270

E. Pollert

Another

situation

d-electrons cannot ge

be

Eel

When

an

exists,

for

oxides

localized

and

consequently

E C + E B ~ O,

the

condition

the

applied

is n o t

also

are

because

fulfilled.

Due

to the

of

the

of

crystal

transitive

ion

of

the

become and

neracy

lowered.

is

matically

element

from

nonequivalent

tic f i e l d

covalency

given

The

the

and

spherically

field

amon~

split

cations

dependence

in Fig.

d-group

are

and

and

of

is

inserted the

the

splitting

Fig.

3.

Splitting fields

magnitudes

of

the

of the

the

ligand

the

correlation

d-orbitals

by

neglected.

their

Then

two

spin

case

terms

in

are

/~ o o r r e l , s t r o n g the

in

her

spin

exceptional

from

4d

levels given

The

low

ions in

by

d I0

and

must

f o r R h 3+

the the

and

cubic

position

d 5 ions

be

of

with

the

its

electrosta-

Orbital

symmetry

is

degesche-

ions

with

oetahedral

of

levels

field,

these

by

the p a r a -

deeidin~A f o r

the

occupation

the

consequently

the g'round lattice.

~eaker,

"Jdn

eolLfi~uration. is

~iven

in

~.

F~xperimental

data

rule

is b r o k e n

and

the

discussed

structures

Co 3+

of e l e c t r o n s

symmetrical

of

III in the of

Ill.

for

the

~plitting

i n Fi~.

ener(~

('Jd6)~

ion

charge

form

~t

r~i-

(3d7),

~+

between of ~n

I:he c a t i o n

t2g Kind is

only

levels.

spherically

e ~ n be

/k e o r r e l > /~c~ ' m e d i u m c a t i o n is Jn the h i g h s p i n

Hund's

e.

of

crystal

the

field

is

ehanc;e

the

is r e v e r s e d .

Distribution

and

characterized

is d e f i n J t e l y

in Table

situation

field,

field.

into

which

and

crystal

A-trigonal

for

introduced

considered

(4d6).

field

consequently

summarized

This

are

distinguished:

for

crystal

state.

splitting

coupling,

the

sequence

is

on

C-tetrahedral

is p r e s e r v e d

usual

/kC~>

anions.

in the

symmetry

effect

are

c a n be

rule

the

the

and

orbit

eases

parameter

field

they

state ease

splitting

the

Hund's

~i%lat is ground

tetrahedral the

of

field,

state.

electrons

of a n i o n w h e n

d-orbitals

field,

of

ir~fluence

the

C

various

and

energy

a crystal

of

eg

= i0 D q

/k

crystal

char-

d

8

B-octahedral

The

model

t2g

\~

A

the

outer

contributions

into

effect

surroundings

dxzCl~

state

The ionic

symmetrical

eovalency

by

e~

of

the

3.

dx,~.z

meter

but

~ O.

orbita!s

Mutual

elements.

particular

Crystal chemistry of magnetic oxides

271

i _Tzul3) _ _7:__ l-4Oq

~, T2Q(3)

dlond cls

j

\

-6 Dq

"

£g(2)

c14and

/

'-'- ~

dg

AzQ(1)

12 Dq

y --.-~- T,,(3) -- ._ I 6._.Dq =

l 6D;lg (3,

J, 20.

Tzg(3)

12 Dq

dZond d 7

Azg(l) d~onclds

Fig.

4.

Splitting the is

case

and

ions

have

hedral -fold

tendency

irLfluenees due

shifted occupied

/3/

by

exist

to c o v a l e n t

states

mixing

p and

s is

with

and

assumption

oxygen

of s t a t e s while

the

/4/,

lowered

/5/

/7/.

of

field.

sp 3 w i t h the

the

sites

orbitals

These tetra-

with

four-

2p c o v a l e n t

energy

for

bonds

tetrahed-

at d 5 i o n s .

covalent

contribution

transitive

centre

energy

/6/,

one

others

the

into

preference

lower

Eel for

crystal

orbitals

are placed

an o u t s t a n d i n g

energy

energies

in

degeneracy

in the

of h y b r i d they

at d I0 i o n s

to the p r i m a r y

of 3d 4 i o n s

orbital

stabilization

combination

fact

the r e s u l t i n g

to h i g h e r

no

and when

the

states

The

in parenthesis.

display

to that

coordination

In contrary

that

Due

ground

field.

to the f o r m a t i o n

/2/,

coordination

are formed. ral

given

consequently

symmetry

of the

octahedral

ions.

of g r a v i t y

the v a l e n c y

It

also appears

of 3d l e v e l s band

formed

by

is

272

E. Pollert

Table

III.

Cubic field responding

Dq

Confi-

gura-

Ion

Compound

tion

3d I

3d 3

Ti 3+

hedral

2030

900

Y3AIs012

2200

1250

1800

840

AI203

1750

AI203

1360

V 3+

V 2+

1180

g

E Soeta

/kJmol-i/

/kJmol-i/

96.7

64.5

90.9

520

780

Stetr~

0

Ref

i 2

104.7

89.6

3

128.5

120.2

i

124.8

0

2

168.3

36.4

1

193.8

0

4

251.2

55.7

1

1825

260.4

0

5

ZnGa204

1800

257.1

0

6

A1203

1810

258. 3

0

7

Mn 4+ Zn2Ti04

2000

285.5

{}

8

Mg2Ti04

2080

296.8

O

8

AI203

2170

309.8

0

9

1760

Mn 3+

2100 AI203

Mn 2+ Na3Mn2Si207 Fe 3+

3d 6

hedral

1905

MgAI204

3d 5

tetra-

and cor-

energies

Dq

oeta-

AI203

Cr 3+

3d 4

of 3d n ions

/cm-i/ /c~-i/

V 4+ 3d 2

splitting

stabilization

930

1947

150.3 139.4

44.4 0

i 2

750

330

0

0

i

796

410

0

0

iO

1400

620

0

0

1

940

0

0

ii

Lio.5AI2.504

1020

AI203

1650 iOOO

440

47.7

31.4

12

Feo. IMgo.9AI204

1250

500

59.9

35.6

12

Fe0.1Mg0.9Ga204 MgO

1200 1030

450

57.4 49.0

32.2

13 2

Fe 2+

2

Crystal chemistry of magnetic oxides

Congigura- Ion

Dq oo~a-

Compound

hedral hedral

tion

/kJmol-1/

Stetra

Ref.

/kJmol-I/

Co 2+

i000 900 950 960

Ni 2+

860 1015

MgAI204 NiCr204 ZnNiSnO 4 Mg0

2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12. 13. 14. 15.

440 410 400 400

71.6 64.5 67.8 68.7

62.8

1

58.6 56.9 56.9

14 12 12 15

27.2 32.2 29.7 30.1

1 16 12 12 17

122.7 144.9

1300

580 450 400

92.9

27.6 21.4 19.3

i 12 12

950 850

450

67.8 60.7

21.4

12 12

CuAI204 CuGa204 Cu0.2Zn0.4Cdo.4AI204 CuZnGe04

87.5

380 452 415 420

870 860

Cu 2+

i. D.S. MoClure,

55.7

1830

MgAI204 Co0.2Znl. SSn04 Co0.2Znl.sTi04 Mg0

3d 9

E Soeta

78o AI203

3d 8

E

/om-1/ /o=-1/ Co 3+

3d 7

Dq tetra-

273

123.9 122.7

J. Phys. Chem. Sol., 20, 311 (1957

D.S. MoClure, J. Chem. Phys., 36, 2757 (1962) H.J. Weber et al, J. Chem. Phys., ~ , 2032 (1971) M.D. Sturge, Phys. Rev., i~O, 639 (1963) D.L. Wood et al, J. Chem. Phys., 48, 5255 (1968) H.M. Kalan et al, J. Chem. Phys., 54, 5197 (1971) R.M.MaoFarlane, J. Chem. Phys., ~ , 4252 (1970) R.Dittman, Z. Phys., 216, 183 (1968) S. Gesehwind et al, Phys. Rev., 126, 1684 (1962) T.F. Veremejeik, Phys. Rev., B~, 3377 (1972) N.T. Melamed, Phys. Rev., B5, 114 (1970) D. Reinen, Structure and bonding, 7, 114 (1970) W. Low et al, Phys. Rev., 118, ill9 (1960) M. Driford, Compt. Rend., 2 ~ , 180 (1966) W. Low, Phys. Rev., 109, 256 (1958)

274

E. Pollert

The

16.

T.

Sakurai,

17.

W.

Low,

situation

is

Chem.

J.

Phys.

Rev.,

schematically

Phys., i__0~

shown

as

~,

2~7

in

3241

(1969)

(1958)

Fi6.

5.

i

3d

i

2s -

o

<',,/, b

Fit.



Effect of

of

the

transition

a-without

Minimalization -

-

of

Preference

of

Nard

to

Tab.

III).

[email protected] Fig.

the

of

the

a

neracy

the

be

achie]md

by

can

motions

of

-- 1{esultin{~" c;ain

Whell

the

Obviously

iierl

end

terms

interael ~lli
of totol

its

ihe

role

[he

kind

in

el'feel,

some

has

5ts

tons

of

stabilizaJ:,ion

surroundinF,

of

[[

Js

lhe

with 15s

re-

(see

shown eub:ie

orbJ. l n l l y

~I t e n d e r m y


\s

field

o<~ses

sites~

enerc:ies

in sym-

decener~ted

it, r e m o v e

i hi s

dece-

/8, .

['elev:~tJl

, i~ el l'{mic

:~t:~t es

/~)z • ~

c,,m[npomise

bel~,{{Jl

ill,

I,,s>

iii {>/;is{ if.:

ener{',:ieb.

refit

ll~s

of

field)

consequences:

specifie

tile c r y s t a l

and

levels

eovaleney,

Jahn-Teller

remain

symmetry

Jhe

the

ener~,,~

[octuhedral

followin~"

their

into

represe<[li:>

electronie

decidinc;

to

t<~ t h e

concentration

poiyhe(iron

the

placed

the

b-with

has

of

on

oxide

cations

UllS t a b l e

surrourldi~lp,

equilibrium in

temperature

ve

state

however

lowerinc;

This

-

is

due are

by

with

and

ions

t[round

system

Eel

magnitudes

symmetry %d

their

Such

term

metal

cevalency~

substituted

relative

/I: w h e n

metry

the

covaleney

~le [ iv~: i,,ll>, }~

J" ~r

syJi]~, [ ~ }r ',~

the,

relnlion

coordinDJiill,

sel,

m~,t;'ni bet~c~n

sn['Vieielll

I u,i,

,,I

lh~

disl

IIi(~ (..[!~e[l'i)ll

l~i|DJ.e I V ,

{hell

bel.~a~

:~ o~'] { Leo !

~ I'' e~'3"si ;iii :i_b l m ~ e r ( ~ d .

'

t~I.[~Oll{[

~iI

t he

~<~IlJ J_~,,llri~t

,~rl J~r~

i~)ll

~J [tee:

])~':)%~iik< ~

v< spect:i-

lJ

[]1<'

O;i.

<~!~(~J~'()~Ib

Crystal chemistry of magnetic oxides

o n the o r b i t a l s in octahedral trated

directed

field

in Fig.

towards

.

.

oxygen

anions,

in t e t r a h e d r a l

i° e. e

field

electrons g as it is i l l u s -

6.

zj [email protected]_~

nearest

a n d t2g e l e c t r o n s

275

~z

z .

i

.

.

.

.

.

.

.

.

.

t

dt

- .......

d~.r= -

d# ~O 1

a,y tiT,

Ca > 1

d~7 - -

c

a

Fig.

b

6. T e t r a g o n a l

distortion

tetrahedron Table

IV.

Occupation

respectively

Configu-

oetahedral t2g

dI

1

eg

levels.

l e v e l s of 3d n ions g and tetrahedral cubic fields

(medium

state)

ration

(a) a n d

energy

of t 2 g a n d e

i n the o c t a h e d r a l

ground

octahedron

of

(b) a n d c o r r e s p o n d i n g

crystal

field,

and Jahn-Teller

field distortion

0

weak

high

spin

distortion.

tetrahedral eg

t2g

1

0

field

distortion weak

d2

2

0

weak

2

0

-

d3

3

0

-

2

1

str o n g

d4

3

1

strong

2

2

strong

d5

3

2

-

2

3

-

d6

4

2

weak

3

3

weak

d 7

5

2

-

4

3

-

d8

6

2

-

4

4

strong

d9

6

3

strong

4

5

strong

276

E. Pollert

2.2.6.

Contribution

optimum taot~

cations

and

of

with

=

the relevant 6-1o]d

in

the

sizes

to k e e p

a sufficient

lattice

parameters

and a steric

2.2.7.

energy

number

of

The

between to b e

their

the

kept.

the m o d e l

=

().31 ~,

zero

causes

us

note

size

ensurin~

mutual of

=

the

close

con-

substituted

the

Theoretical

radii

of

the

;~i'~ ~tn a p p r o x f m a t e

of h a r d rvi

of

spheres.

Using

~uide

the v a l u e

0.58 ~ and rXi I

=

1.I~0

in

at

we

tions

have on

equilibrium (14)~

we

hand

state

for

the

above

all

relation

exchange

entropy

with

term

the

with

to

their

of

the the

which

an effort

theft t h e

ideal

positions

at

the

form

~n

both

the the

contributions ordered

state.

tendeneies.

temperatures

close

temperatures

in an increase

are

of

increase

often

of

in

the

the

corresponding

to

where

symmetry.

state

to

tile

of

a

entropy

preparation.

sublattices

mutual

G

to

properties

the

to

at h i ~ h e r

materials

the

lowering

against

between

important

interplay

entropy ~

acts tend

resulting

of

the

tendency

is n e g l i g i b l e

studied

in

it which

quenched

cations

to

the

compromise

term becomes

= A(%

individual their to

from

Due

term

=

0

of

TS

on

holds.

the

Then~

LC,

Eel

and

other using

hand relations

pV

contribu-

leads

to (13)

the and

write

An

where

to~ether

term pV.

contribution

changes

above

one

can

Its

temperature

mentioned the

the

shifted

Consequently

with

of

are

connected

a

fact

the

Distribution

is

transitions

equilibrium

contribution

ions

represents

this

these values

appears.

volume

the

but

from

influence

entropy.

and

that

energy

states.

structural

metastable

of c a t i o n s

crystal

energy

importance

2.3.

a

equilibrium

absolute

An

of

ohan~ed~

of

of

internal

Let

are

equivalent

Resulting

As

has

condition is

]2-1',~ld c o o r d l n a t i o n ~

riv

bond

distortion

Contribution

Gibbs

it

holes

anions

obtained.

Deviations

of

proportion

and

the radii

Important

surrounding

limitation

to t h e

I.~0 X

c h a nn~es..

and

adequate

~-feld~

regard

r02_ are

of v o l u m e cation

Consequently

holes with

amon~

bond

the

of

.

two

~el )

contributions

ealenoy~ ~iven

~:B +

eleetronie

crystal

cations

+ p&V

depend

=

on

(15)

TAs

the properties

configuration

and

size

structure.

between

two

different

sublattices

of

cations 7

( T a b l e V)~

in

Crystal chemistry of magnetic oxides

/(Mel)a-~ can be expressed

(Me2)~ /A /(Mel)~

(Me2)b- 6 / B O z

by the r e a c t i o n

(a- 6 ) ( M e l ) A +

(b- ~ )(Me2) B

is the d i s t r i b u t i o n

where

277

=

parameter

(16)

~ (Mel)B+ j (Me2) A

of cations

between

the both s u b l a t t i -

oes.

Change

of the Gibbs

energy

connected

w i t h this r e a c t i o n

is

~2 A

G

=

A

Ho _ T ~ s o

+ ~ T in

(17)

(a-~)Cb-J) where

/kH ° = f k H e x , enthalpy

the c a t i o n from the first

change

oe, w h i c h may be interpreted of cations

with

PMe 2 -

=

In the e q u i l i b r i u m

In c o n s i d e r i n g

ex

=

of cations

dent v a r i a b l e s

energies

/16/:

(18)

between

the exchange

on the sublattices

R T Zn

( a - ~)(b-

w i t h S sublattices

analogous

are obtained

of

sublatti-

enthalpy

and the equi-

A and B is obtained:

~2

TAS °

a crystal

(S--IXP--1) equations

exchange

of the second

of the p r e f e r e n t i a l

sublattioe

-

A H

the mutual

PMe I

the r e l a t i o n

distribution

with

one c a t i o n

as the d i f f e r e n c e

Me I and Me 2 for a particular

/kHex

librium

connected

sublattioe

(19)

~ )

containing

to the r e l a t i o n

(19) for

P various (S-I)(P-I)

ions. indepen-

/17/.

Table V. Cations

in oxidic

spinels,

perovskites

and

magnetoplumbites

Atomic number

Monovalent

Cation

Configuration

Ionic radii

of outer

coordination

electrons

in I.

Struo-

4-fold

6-fold

12-fold

ture2

3

Li+

i s2

0.59

0.76

1.235

S,P,M

ii

Na +

2P 6

0.99

1.02

1.39

S,P,M

19

K+

3P 6

1.64

P

29

Cu +

3d I0

0.60

0.77

S

278

E. Pollert

Con£iguration Atomic

number

Monovalent

Divalent

Trivalent

Cation

of outer electrons

ionic r a d i i coordination

in i "

Struc-

t u r e 2"

4-fold

6-fold

12-fold

1.00

1.15

1.53

S,P,M

1.70

M

0.57

0.72

37

Rb +

h p6

47

Ag +

1;d 10

81

TI + M g 2+

6s 2

12 20

Ca 2+

3p 6

25

Mn 2+

3d 5

0.66

O. 83

S,P,M

26

Fe 2+

3d 6

0.63

0.78

S,P,M

27

Co 2+

3d 7

0.58

0.7t45

S~P,M

28

Ni 2+

3d 8

0.55

0.69

S,P,M

29

Cu 2+

0.60 0.60

0.73 0.7h

S P ~M

2P 6

30

Zn 2+

3d 9 3d 10

38

Sr 2+

f4p6

48

Cd 2+

14dlO

56

Ba 2+

9P 6s 2 6 2p

82

pb 2+

13 21

kl 3+

Sc 3+

22

Ti 3+

23

.

P

1. O0

1.18 0.78

P,M

S M

1 . 111

P,M

1.61 1 .h9

P M

0.95

6

P

P M

S P,M

3p 6

0.535 0.745

3d I

O. 67

S P,M

V3 +

3d 2

0.6I~

P

24

Cr 3+

3d 3

0.615

P~M

25

Mn3+

3d lI

0 . 645

P~M

26

Fe 3+

3d 5

27

Co 3+

3d 6

31

Oa 3+ y3+

3d 10

39

0. h 9

0.tt7

Rh ~+ i n 3+

%d6

57

La 3+

5p 6

58

Ce 3+

4d I0

S P~M

0.62

S P~M

0.61

P

o . 62 o. 9

4p 6

49

45

0.39

S,P~M

1.3q

S

1.19

0. 665 0.62

S~P

0.80

1.o3

P~M

P

S~PgM i.36

P ~M

6s 1

I. 3!~

p, ~r~)

59 60

p r 3+

5p6~If 2

I. ]}0

P~M

Nd 3+

1.27

P ~M

6i

pm 3+

5p64f 3 5p64f 4

62

Sm3+ Eu 3+

5p64f 5

1.2h

P ~M

5p61~f 6

i. 22

P~M

64

Gd 3+

5p61~f 7

I. 2 i

P

65

5p64f 8

1.20

P

66

Tb 3+ Dy 3+

5p64f 9

i. 19

P

67

Ho 3+

5o61~f I0

i. 175

P

63

?

Crystal chemistry of magnetic oxides

Atomic number Cation

Trivslent

Tetravalent

Pentavalent

Sixvalent

Sevenvalent

279

Configuration Ionic radii in of outer coordination I" Strueelectrons 4-fold 6-fold 12-fold tures2"

68

Er 3+

5p64f II

1.15

P

69

Tm 3+

5p64f 12

1.14

P

70

Yb 3+

5p64f 13

1.13

P

71

Lu 3+

5p64f 14

1.12

P

81

T13+

5d 10

0.885

83 14

Bi 3+ Si 4+

6s 2 2p 6

1.03 0.40

22 23

Ti 4+ V 4+

3p 6 3d I

0.42

0.605 0.58

S,P,M S,P

25

Mn 4+

3d 3

0.39

0.53

S,P

32

Ge 4+

3d I0

0.39

0.53

S,P,M

40

Zr 4+

4p 6

0.59

0.72

P,M

43

To 4+

4d 3

0.645

P

44

Ru 4+

4d 4

0.62

P

50

Sn 4+

4d I0

0.55

0.69

S

72

Hi"4+

5p64f ]4

0.58

0.71

P

77

Ir 4+

5d 5

0.625

M

0.26

P

1.45

P,M S

90

Th 4+

6p 6

0.94

1.21

P

92

U 4+

6p65f 2

0.89

1.17

P

23 41

V 5+ Nb 5+

3p 6 4p 6

44 51

Ru 5+ Sb 5+

4d 3 4d I0

73

Ts 5+

5P 6

0.64

P

76 42 52

0s 5+ Me 6+ Te 6+

5d 3 4p 6 4d l0

0.41

0.575 0.59 0.56

P S P

74

W 6+

5p 6

0.42

0.60

P

75

Re 6+

5d I

0.55

P

76 92

0s 6+ U 6+

5d 2 6p 6

0.545 0.73

P P

43

To 7+

4p 6

0.56

P

75

Re 7+

5P 6

0.53

P

0.355 0.48

0.54 0.64

S,P P

0.565 0.60

P S,P

i. R.D. Shannon, Aota Cryst. A_/~, 751 (1976). 2. Landolt-B~rnstein, 4a~ b, Magnetic and Other Properties of Oxides and Related Compounds, Springer Verlag, Berlin-Heidelberg-New York (1970).

280

E. Pollert

3.

Cations~

which

tetrahedral layers. gen

The

layers

c a n be p l a c e d

sites~

enter

periodicity and

three

with

into of

the

the

spinel

SPINEL

STRUCTURE

regard

to

their

fundamental

lattice

blocks

is

sizes

matrix

given

respectively

by

in

the

formed

the

(Fi~.

oetahedral

by

the

sequence

of

7).

C

S

Fig.

7.

Formation pation cations

hedral

of

the

spinel

of

tetrahedral

0

-

oxygen

position

positions

(B).

structure and

anions~

(A),

by

octahedral •

-

cations

O - cations

the

occu-

holes

in

in

by tetra-

octahedr~l

or

oxygen six

oxy-

Crystal chemistry of magnetic oxides

Basic

contribution

of c a t i o n s

the m i n i m a l i z a t i o n for

its

i n Fig.

in the l a t t i c e

of the C o u l o m b

explanation

energy

the u s u a l r e p r e s e n t a t i o n

8, S p i n e l

structure

in the l a t t i c e tion

position

32e~

sitions~

~-

tions

It is b a s e d

on the face

tion between tetrahedral

cations

with

of c a t i o n s

occupied

The

Another four

leads

structure

to u s e given

among

situation

penetrating

-

are AA

anions

in 8a t e t r a h e d r a l positions~

in po-

O - ca-

[]- 16o

oota-

by

exists

with

cubic

ions~

lattices,

of o x y g e n a

2

of

anions =

in the <100>

Connection

of two

i n the a r r a n g e m e n t

structure cell

total number

(see Fig.

containing

97. 32

of 64) a n d

16

centered

cubic

of 32).

two p e n e t r a t i n g

i n the body

occupancy

separated

elementary

the

(mutual rela-

the r e q u i r e m e n t

~,

place.

but d i f f e r i n g

of the s p i n e l

octahedral

The by

=

are

one v a c a n t

cubic

form

i).

~

cell

1 a.~

centered

a

~,

positions

(from

anions

at g i v e n r a t i o

the t o t a l n u m b e r

positions

mutually

see Fig.

form

sites

(from

of o x y g e n

is c o n t r o l l e d

=

of a n i o n s

tetrahedral

face

B-sites

anion and

alternating

tetrahedral

shifted

oxygen

positions

structures

in o c t a h e d r a l

oxygen

sites

O-

lattice

the c a t i o n s

distances

to the p r i m i t i y e

octahedral

of cations

to the m i n i m a l i z a -

energy

cations

cubic

packed

arrangement

regularly

8 occupied

occupied

lattices

about

positions.

cations

by one

the same

cubes

anions,

that

•-

ootahedral

(minimum

always

distribution

8b t e t r a h e d r a l

centered

distances

4:3

Let us n o t i c e direction

and

basic

in 16d o o t a h e d r a l

foe a n d close A-sites

of the m a x i m u m

Eight

an effort

It is s u i t a b l e

of the s p i n e l

with regard

of the C o u l o m b

hedral

cubes

from

contribution.

8.

Fig.

and

results

281

diagonal

which

face

direction.

c a n be d i v i d e d

Each from

into

them belongs

to one

282

E. Pollert

Fig.

from ry

the

of

ing

Primitive

equivalent

the

as

responds

ions

Howe~er

the

is

of

axis

space

so

~

that

~roup

the

tri~onal

in the whole

symmetry

to

cell

direstions

octahedral

cations,

equally

9.

0~

spinel

<~ii>~

~

due

the configuration

lattice the

structure.

to

cell

o~erall

.

all

symmetry

The

local

directions

remains

symmet-

of s u r r o u n d occur

cubic

and

eor-

(Fd3m).

-~-

-4

Q

4

Fig.

The

oxygen

to i t s

can

shifted

hedron mined

in by

hedral

where

and

a is

u

has

As

it

i n the d i r e c t i o n

elementary

cell.

oxygen parameter = 0.375.

The

octahedral

of t h e

anion

a particular

properties.

the the

the value

Environment

sublattice

regard be

i0.

rA

:

(u

rn

=

(~ - u)a

the

lattice

in

the s p i n e l

demonstrated

of

the body

dia~onal

The

position

of

u which

whose

_ 7)a.671

position

is

shifting

holes

in spinel,

in

causes radii

the

in FiG.

oxygen

case

changes are

of

~iven

of

the

the

with anions octa-

then deterstructure

dimensions

has

of t e t r a -

expressions

(2O)

- r02_ of

is

ideal

_ tO2-

constant

oxygen

the relevant

anions the

in t h e by

i0

l~ttice

(2i) the

cubic

spinel

lattice.

Crystal c h e m i s t r y

Consequently bility

magnitudes

of the

of b o t h

substitution

types

into

the

with

radii

size

of s u b s t i t u t e d

cations

and

the

of the

sizes

from and

(21)

cations the

comparison

experimental

i n Tab.

linear

radii

in the a p p r o x i m a ± i v e

and

od A a n d B i o n s

spheres

(Fig.

seems

spinel

- i°15 of the

of h o l e s ,

slightly

is

equal

extended

oxygen

from

at

the

is

obvious

expressions of

(20)

the r e l e v a n t

the s u b s t i t u t i o n

on t h e r e d u c e d

applicability

a possi-

between

parameter

the r a d i i

contracted

and

to c a t i o n s

~. R e l a t i o n

calculated

parameter

justify

283

become

of ~ a n d u, w i t h

oxygen to

may

lattice

0.35

the v a l u e

are

of the

oxides

of h o l e s

range

values

~-~. C a t i o n s

dependence

of magnetic

but

difference

of the m o d e l

of

of h a r d

ii).

u

4-2 type

2-3 type e G O 3'

0.39

+AI3'

o sn4*

nV 3+ vCi-)*

v Ti4°

+ 1

• ~lr'~

AFe z'

0.38

i 0.37 • No,w0,

AgzMo04

0.36 -GO8

-o.o~

-0.00

-o~

o

OOl o

Fig.

An

extreme

into

the

small

ion

case

oetahedral

the

preference

placed

cations

Consequently

of r a d i i

the

leads

oetahedral

can

to

conclude

for

this

case

the the

position

from

sites

of C d V 2 0 4 sites

/10/.

subtitution

(u = 0 . 3 6 4 ) .

tetrahedral

that

by

fact,

ootahedral

in the

u on the r e d u c e d

of A a n d B i o n s

is f a c i l i t a t e d

tetrahedron

small

parameter

by A g 2 M o O 4 w h e r e

M o 6+. D u e

of the

(4d lO)

the

one

positions

of V 3+ ions

into

towards

of the

difference

ions

centre

of C d 2+ ions

large

Dependence

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

tetrahedral

towards strong

ll.

and

of s i l v e r

presence

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

oxygen

anion

is

On

other

hand

and

the

electron

to the the

ions

shifted the

configurat-

substitution

oxygen

anion

(u = 0 . 3 9 4 ) °

the

steric

point

of v i e w

for

of

is d i s -

the

284

E. Pollert

substitution in the spinel lattice not only absolute size of the respective cations is important but also the relation between them determining the distance

(Me')A- 0 - (Me'')B o Table VI. Comparison of radii of A and B interstices R calculated using experimental values of lattice parameters

a and oxygen parameters u

with corresponding ionic radii R M (all in ~)

Distribution

Spinel

a

A

u

of ions

R

B

RMe

R

RMe

ZnFe204

Zn2+/Fe~+/

8.433

0.3852

0.575

0.60

0.622

0.62

NiFe204

Fe3+/Ni2+Fe3+/

8.33

0.3822

0.507

0.49

0.622

0.655

Fe304

Fe3+/Fe2+Fe3+/

8.394

0.379

0.475

0.49

0.665

0.70

MnCr204

Mn2+/Cr~+/

8.437

0.3889

0.63

0.66

0.592

O.615

ZnCr204

Zn2+/Cr~+/

8.321

O.3863

0.564

0.60

0.586

0.615

FeV204

Fe2+/V~+/04

8.453

0.386

0.59

0.63

0.62

0.64

LiV204

Li+/V3+V4+/

8.22

0.385

0.522

0.59

0.573

0.61

Co2GeO 4

Ge4+/Co~+/

8.318

0.375

0.39

0.40

0.679

0.745

Mg2Ti04

Mg2+/Mg2+Ti4+/

8.441

0.3875

0.61

0.57

0.605

0.61

Na2WO 4

W6+/Na~/

9.13

0.369

0.48

0.42

0.937

1.02

3.1. Distribution of cation between tetrahedral and octahedral sites

The distribution of cations in the spinel Mel/Me2/204 can be, in analogy to equation (16), expressed by the general formula

/(Mel)l_ where If

a

A

and

large

B denote

~ (Me2)~/A tetrahedral

difference one

type

/(Me2)2_

between of

sites,

and

~(Mel)

~ /B04

oetahedral

the

preference

the

exchange

sites energies

enthalpy

respectively. of

exists

for

decides

bution

of cations, q~nen the spinels with normal structure

cations about

Me I and the

Me 2

distri-

/Mel/A/(Me2)2/BO 4 (~ = 0) or inverse structttre /Me2/A/(MelMe2)/B04 (j = i) are formed. On the other hand when the difference between the preference

Crystal chemistry of magnetic oxides

energies tropy

3.1.1. in

is n o t

term

and

too

Exchange

oxide

large,

the d i s t r i b u t i o n

a tendency

to m i x e d

enthalp~.

spinels

is

The

is r a t h e r

structure

largest

the C o u l o m b

controlled

appears

by

the

en-

(0<6~1).

contribution

energies.

285

to the

Its magnitude

internal

is g i v e n

energy

by

the

U

ex-

pression



where lung

e is

=

the

in

which

one k i n d

oxygen

parameter

several

authors

/14/

(e2/a)

charge

constant,

present

-

leads

of e l e c t r o n ,

of s i t e s

u. H e n c e /ii/,

The

=

/12/,

follows

12. A s

spinels

use

of the

a n d A M the M a d e -

charge

in A-sites function

of c a t i o n s

qA ) a n d

was

generalized

- 6483~2u

- 1903~2u)qA

the Fig.

The

dependence

with

2-3

containing

+ 2.609

increasing

of t h e

calculated ~wald

by

method

2 qA

(23)

containing

the

the the

of the

Madelung

takes

places

for

constant

large

of

qA < 2 a n d

of t h e s i z e cations

However,

of the C o u l o m b

the

u is given

constant.

it is p o s s i b l e

experimentally.

parameter

on the v a l u e

divalent

cations

influence

oxygen stability

an influence

tetravalent

confirmed

2 < q A < 3,

of

value

of the M a d e l u n g

spinels

was

this c a s e

12

values

E C is n e g a t i v e ,

simultaneously

small

which

all for

various

energy

with

from

distribution above

The

parameter

electric

of c a t i o n s

= 139.8 + i 1 8 6 ~ u

the

parameter r e f l e c t s

Therefore

mean

A M ( q A , u ). T h i s

/13/.

of A M on qA f o r

i n Fig.

pectively. gen

=

+ 412.2~Iu

arrangement i n c r e a s e s

As

(usually

AM

lattice

of the

u - 0,375,

dependence

given

a the

to the f o r m u l a :

- (10.82

~u

(22)

is a f u n c t i o n

A M = AM(qA,u)

where

AM

qA > 3 r e s of the

oxy-

of c a t i o n s .

and with to e x p e c t

4-2 normal

i n many c a s e s ,

contribution

is n o t

unambiguous.

The of

contribution the

simplest

of the B o r n 2-3

type

by

repulsion the u s e

energy

of the

c a n be

empirical

estimated

for

spinels

formula

= (Bxx/an)/4 (a/rA)n + 6(2- ~ )(a/rB)n/ * • (Blll/an)/4(l- 6)(a/rA )n + 6 (a/rB)n/ where

BII , Bi11

are

experimentally

determined

parameters,

(24) related

to M e 2+

286

E, Pollert

and in

M e 3+ c a t i o n s tetrahedral

respectively~

and

rA/a , rB/a

octahedral

positions

relative

cation

respectively

- anion

Given

by

the

distances express-

ions:

rA/a

~(U

: =

l ~)

{ 2~ )

-

+

-

2

~26)

A~

] !

142 140 138 136 134 13; 13[

,%

12E 2

Fig.

12.

Dependence ge

ionic

values

The

contribution

cations

in

Eel

of M a d e l u n G charge

of

is g i v e n

by

the

respective

Eel

= - /ES,A(Mel)/(1-

contribution

deformation

of

pV the

sites

of

the

lattice

of

the

substituted

tributions

Then ly

parameter.

E C and

neglecting

(like

(elastic oxygen

cations

qA

the

~*

constant

Tab.

on

ions

tile a v e r a for

several

u.

stabilization

{see

energies

of

the

individual

Ill):

J ) - /ES,A(Me2)

+ ~S,B(Mei)/~

~)

enerG3r)

is f o r

sublattice

(oxygen

Consequently

is

qA

of A - s i t e

the p a r a m e t e r

- /BS,B(M%)/(2The

3

covered

the m a j o r

part

parameter)

a n ini'luence

substantially

minimized

and

by

the

of

the

by

oonsiderin~

by

the

changes

different

sizes

the

con-

E B.

the

influences

contributions

which

of o o v a l e n o y ,

are

dif£icult

polarization

to d e s c r i b e and

the

quantitative-

term p¥

itself)

Crystal chemistry of magnetic oxides

the v a l u e s

of

the

exchange

enthalpies

c a n be d e r i v e d

287

from

the

equation

/6/,

/15/ Hex

= /P(Me2)/B

- /P(Mel)/B Eel~

EB

The values are

given

of p r e f e r e n c e i n the Fig.

~H (~---'~-)6 = 1 / 3

=

energies

(28)

calculated

according

to

the

equation

(28)

13 /15/.

,

-20C

,

,

,

,

,

,

,

,

,

,

,

i

,

,

,

,

,

,

/

PIMe]

pJ/too! -15G

o/ -~.0~

-5C

.

.

Zn2÷

.

.

3. Cd

Fig.

13.

Let

us

seems

meter

note

that

not

u = 0.3822

=

u

for

the r a n d o m

the v a l u e cations

experimentally

are

2* hi

~

*

i

i

t

2*

Ti

3* CO

i

I

i*

2,GG z,Fe Fe Mg

energies

P,

simplifying

from

- O.0!2qA

distribution

in tetrahedral

i

Mn

correct.

following

0.407

they

+ Cu

t

I

~

I

l° 3÷Cu 2*

i

I

~.

~ N, Cr AI'* Mn 3°

V

[email protected] - /6/,

- O-



/16/,

/19/.

quite

of u a c c o r d i n g

Nevertheless the

-

the n e e d f u l

to be

,

*

Ag

Preference -x

ion

.

2*

In

to

the

positions

it

is

used

the

in the

constant

calculat-

oxygen

para-

/18/

+ 0.001q~

(29)

in the

relation

only

and

not

in relatively

determined

all

equation

of e a t i o n s this

presumptions

Above

does

good

2-3

influence

agreement

distributions

spinels

depends

with

of c a t i o n s

(qA = 1/3)

on the m e a n by

their

values

because

charge

obtained

in spinels

of

size.

with

from the

288

E. Pollert

mixed

structure

/16/

and

with

those

calculated

it

supposed

from

the

thermodynamic

data

/19/. 3.1.3. is

Entropy

changed

while (26)

in the

standard critical

roughly

a good

te~

the v a l u e

However~ entropy

course

value

of

the

change

of

AHex

If

mobility

this

Usually

entropy

estimated.

for

the

term.

the

of

is

exchange

of

waranting

of ~ H e x ~ 1 0 . 5

kJ/gatom

approach

quite

~ S ° are not

thermodynamic

Table

is n o t

negligible.

data

are

VII.

sitions sites

4.1.

It

seems

ding It

for

the

Table

ehenge

of

tetrahedral

the

tion

- 14.1 - 17.6

Ni 2+

-

A I 3+

- 10.9 - 17.2

C u 2+

-

EXAMPLES

derived

Neorg.

OF S P I N E L

to s t a r t of

the n o r m a l

/20/,

/21/

Coulomb

the

the

standard

cations

from

VII.

the

cation

and

tran-

octahedral

-~octa)

- - 29.J

1

materialy

13,

COMPOUNDS

with

AND

MgAI204

1669

SOLID

because

A13+

materials

normal

of c a t i o n s

contribution

Consequently

originally

isostructural

or n e a r l y

distribution

energy

ions.

of

some

(1977)

SOLUTIONS

spinels

group

of b o t h

sta-

5.4

Co 2+

the

limiting

spinel.

Si 4+

the

in which

be

equilibrium

changes

Fe 3+

to be u s e f u l

as

and

can

/Jgatom-lgrad-i/

Reznitskij,

and

to w h i c h

has

/23/ by

MgAI204

the

because

in

(25)

obtained.

S ° (tetra

4.

of

determined

entropy

ion

L.A.

considered

entropy

sublattiee

structure

values

between

in the

of m i x e d

attainment

is

the

equations

rightful

The

summarized

Standard

the

1 0 0 0 K is

the

configuration

between

using

the f o r m a t i o n

temperature

only

of c a t i o n s

~ S ° = 0. T h e n for

ions

that

ions

of

the

occupy

mineral

- spinels

structure

between

natural

with ~

A and B-sites 2p 6 e l e c t r o n i c the

oetahedral

accor-

- is n a m e d . 0.i

/22/,

is d e t e r m i n e d configurasites.

The

Crystal chemistry of magnetic oxides

larger M g 2+ ions h a v e tively h i g h v a l u e spinels where

to be p l a c e d

a small d i s p l a c e m e n t

ions a l o n g a < i l l > direction, / 2 4 / was

in t e t r a h e d r a l

of the o x y g e n p a r a m e t e r

true

"spinel"

sites

at h i g h e r

and at 720 K it t r a n s f o r m s

tem-

to the

all three s p i n e l types:

i n v e r s e and m i x e d are obtained:

ture r a n g e

ZnAI204

0.94

~ 6

~

o.96

147o K

t

NiAI204

0.07

~ 6 ~

0.26

868 K

t

1664 K

CuAl204

0.64

< 6 <

o.68

886 K

t

1468 K

covalent

of c a t i o n s

correspond

practically

1173 K

in the g i v e n t e m p e r a -

/26/.

to those expected.

Zn 2+ (d I0) ions

b o n d i n g in the t e t r a h e d r a l p o s i t i o n w h i l e N i 2+ ions due to

electron configuration prefer

Similar

(its v a r i a t i o n ) ,

( m e a s u r e d on the q u e n c h e d samples)

The d i s t r i b u t i o n s their

octahedral

equivalent

s t r u c t u r e w i t h space g r o u p F d 3 m /25/.

w h e r e ~ is the d i s t r i b u t i o n p a r a m e t e r

favour

coordinated metal

The n o n e q u i v a l e n t

statistically

of t h e r m a l v i b r a t i o n s

to r e l a -

is one f r o m the

l e a d i n g to the space g r o u p F ~ 3 m

W h e n m a g n e s i u m ions are r e p l a c e d by s u i t a b l e c a t i o n s normal~

MgA1204

of the o c t a h e d r a l l y

o b s e r v e d and s t u d i e d in detail.

because

sites w h i c h leads

u = 0.388.

(off oentres)

of the r o o m t e m p e r a t u r e p h a s e b e c o m e perature

289

no p r e f e r e n c e

octahedral positions

and C u 2+ (d 9) have

and can be p l a c e d in b o t h sites.

s i t u a t i o n can be o b s e r v e d if A I 3+ are r e p l a c e d by p r o p e r

M g C r o 0 h has

the n o r m a l

Cr D+ ions to occupy

structure with regard

octahedral positions,

(4d I0) leads to the i n v e r s e

structure

cations.

to the v e r y s t r o n g t e n d e n c y

the s u b s t i t u t i o n

and MgGa204

of I n 3

of

ions

is a m i x e d s p i n e l w i t h the

d i s t r i b u t i o n M g n iRGan R g / G a l iRMgn Rg/0h /27/. The e x p l a n a t i o n of the last ............... i0 ~ 3+ lons~ but e x a m p l e is not clear b e c a u s e of the 3d c o n f i g u r a t i o n of C-a •

~

there is p r o b a b l y increase

,

an i n t e r p l a y

of sterio

of the sum of m e a n ionic r a d i i

respectively)

and o o u l o m b i c

.

(mixed s t r u c t u r e of ions p l a c e d

leads

to a slight

on A a n d B - s i t e s

contributions.

4.2. F e r r i t e s

4.2.1. M_aalletite. nel's

group,

It has gies

Fe304,

magnetite

rature

of the most i m p o r t a n t

spi-

ferrites.

the i n v e r s e

structure

Fe3+/Fe2+Fe3+/04

of Fe 2+ and Fe 3+ cations.

perature

is the b a s i s

are r a n d o m l y d i s t r i b u t e d

of the V e r w e y

due to the p r e f e r e n t i a l

Ions on B - s i t e s

transition.

and b e c o m e Originally

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

o r d e r e d b e l o w 119 K~ a charge

ener-

elevated

tem-

the t e m p e -

ordering scheme in

290

E. P o l l e r t

which in bie

Fe 3+ a n d Fe 2+ i o n s

alternating

layers

distortions

cations

were

arising

assumed

form

along from

/28/,

chains

the

lined

c-axis

the

up

(see

in < [ i 0 >

and

Fig.

14)

and

of

the

sizes

differenoies

a



directions

small

orthorhom-

of

the

ordered

/29/.

0 0o0 0o0 cO 0 o 0 0 o 0o0 0o0 0 0o0 0o0 0 0°0 0o0 cO 0 o 0 0 o 0o0 0o0 0

O.O ( 0 0-0 •0 0.( 0-0 0

-o

oO.OC . 0 0 0 0 ( )o°o O. OoO o05?0o8?0 %OoO

Fig.

14.

Electron tively O-

The recent

detail

gement

given

clinic

than

~p

Fig.

orthorhombie

= spinel),

space

group

ring below TV are Coulomb led

of C a a n d C b p l a n e s r e s p e e s model /28/ O02 , @ - Fe3+,

Fe 2+.

structural

in t h e

ordering

in V e r ~ e y

studies

15 a n d with C2/o

the

/30-32/ structure

showed, was

a =

a .~, b = b .~, sp sp /33/. The major forces

interactions b u t f u r t h e r

however

found

another

to be r a t h e r

c = 20 , ~ <~.~ 90 ° , sp i n v o l v e d in the o r d e -

contributions w e r e r e v e a

/341. • 0 0• 0 0 0 0o [email protected] 0 o00 0 00 •0 0 o 0 0 0 0 0 0 0 ~ 00 0 0 @0 0 0o uO0000 0o 0 o0• 0 0o 00 0 o @ 0 0 0 0 0 0 O •~ •O 0 [email protected] O • Q uO0000 0• 0 00 o 0 0o •0 0 o @ ~OOOOOO ~00.O O.O O uoO 0 o 0 0 o 0

Fig.

15.

0o00"00o00 -0~,0o0_0o0 (>o u uoO 0 o 0 0 ~ 0 0o0 0.00oC) 0.0 0.0 0.00 o O O . O O o O C)O 0o0 0o0 0~0 ~ .• O• 0 0 0• 00 C • • ) J O 0 0 0 0 0 •O 0 o 0 O ' O Clo D 0o0 0o00oO

D°.S°o°.tOo.O&Oo

Electron ordering of Ca and tively in MizoguohiSs model @_ Fe 3+, O- Fe 2+.

arranmono-

C b planes /30/ O-

respec02- ,

Crystal chemistry of magnetic oxides

Small

substitution

Verwey

transition

impurities reason

is

of this

the

different the

effect and

size, iron

most can

The

Ga 3+

the

into

for

itself

is n o t

the

changes i n the

and

in

electron

the

temperature

critical

of i m p e r f e c t i o n s

Co 2+, A 1 3 + ,

temperature

Ti 4+

ions

influence

A-sites

From

perceptibly

valency

of N i 2+,

a n d M g 2+ i o n s

tuted

lies

lowers

a certain

the m e c h a n i s m

the r i s e

transition

pronounced compare

Even

when

entirely

of

of

clear

the

the r a t i o

ordered

configuration

of the

concentration

phase

of c a t i o n s

due

to

which

ions.

q~ne s u b s t i t u t i o n example.

in

non-stoiohiometry

disappears

obtained.

Fe 2+ / Fe 3+

replace

or o x y g e n which

291

because

of Ga 3+,

tend

to f o r m

Cr 3+ a n d Ti 4+ i o n s

gradually of t h e i r

M g 2+ a n d

mixed

decreases high

B-sites

the

valency.

Z n 2+ i o n s

spinel

into and

Similarly

respectively.

structure.

is a n

effect

Zn 2+ ions

is one

While are

substi-

only.

the p r e s u m e d

distributions

of c a t i o n s :

G 3+ ~ 3+ i~ 3 + ~ 2 + _ 3+ i^ ax_y~el_x+y/Uay ~e ~el_y/U 4 2+ 3+ 2+ 2+ 3+ Mgx -y F e I -x +y / M --y ~ F e ~~ - x F e I +y / 0 4 2+ 3+ 2+ 3+ Zn x F e l _ x / F e l _ x F e l / x / O

one

can

tant

intuitively

in

the

Critical

considered

Let

x = 0.4

4.2.2.

that

for

decrease

of T V h a s

the d i s a p p e a r e n o e

about

however

measurement

0.1

that

ions

using

to be

of the V e r w e y

of i m p u r i t i e s

M~ssbauer

a transition

at T = 30 ~ i0 K

Substitution

the

in the

simplest us n o t i c e

in

in c o n t r a r y

of divalent

energies ce

of the

dependent is d u e

cationSo

of F e 2 + / F e 3+ r a t i o

distribution

to the r e l a t i v e l y

of c a t i o n s small

of Fe 3+ a n d M g 2+ r e s p e c t i v e l y entropy

term.

A

structure

Mgo.iFeo.9/Mgo.gFeo.i/04 is

and

MgxFe3_x04

Let

That

spinel

speetrosoopy system

The

tem.

impor-

is

formula the

was

initial indicated

/36/.

inverse Fe/FeNi/0 h spinels. ~ 2 + - 3+ 2+ 3+ Zn x F e l _ x / F e l _ x F e l + x / 0 4 series causes

Z n x2+.. 2+ ~..3+~0 Mgl--x/A±2 / 4 a variation

transition

per

Zn/Fe~/O& a n d

Temperature

the m o s t

/35/.

to be

us n o t e

permeability for

expect ease

concentration

usually unit.

latter

4

reported

close for

exists

consequent to the

MgFe204

that

to

in

are n o r m a l

the

substitution

the p r e v i o u s

in ootahedral

difference

and

examples

example

sites

the M g x F e 3 _ x O 4 s y s -

between more

inverse at 4 0 0 ° C

the preferential important

one~

influen-

in particular

/37/,

but

when

the

292

E. Pollert

temperature and

the

type

An

is

sites

leads

8.376

~

to

of

the f r a c t i o n

to

the

towards

(more

or

the r a n d o m

less)

from

distribution

an inverse

appears

to a m o r e

normal

Similar

results ions

ions.

were

only

1470

K were

down

from

the

C d 2+ i o n s

This

be

is

less

B positions

the p V

it

ions

lattice

from

favourable Fig.

system

on t e t r a h e d r a l

constant

770 K and

2-3

times

be

seen

to

the

be p o s s i b l e true

mutual

from

1520 K respecti-

higher

in

the

small

of x i n c r e a s e s ,

i.

e.

the

becomes size

their

the

~

-

of

where

of

the

in

is the

least

only

of

than

tetrahedral

partially

placed

o[A]

-

80 6( 8.3

4C

20

Fig.

16.

0.6

Occupancy

degree

trice

lattice

and

system. ®constant.

0.4

0.2

of C d 2+ i o n s constant

A-sites,

in

each

subla-

in C d l _ x N i x F e 2 0 4

O - B-sites,

anions.

possibility larger

in

tetrahedral

oxygen

100

0.~

cooled

Cdl_xNixFe204

concentration

higher,

at

the

16).

%

quenched

samples

presence

of x,

of N i 2+ i o n s

are

of

shifting

of C d 2+ i o n s

a n d C d 2+ i o n s

in

configuration

values

the

placing

than

as

of M g 2+ a n d

in s a m p l e s

ease

electron

by

because

Ni 2+ act

of 6 0 K h -I / 4 1 / .

to e x p e c t

for

where

distribution

on A - s i t e s

the r a t e

can

is

NixMgl_xFe204

the

enlarged

Consequently

(see

by

in B p o s i t i o n s

supressed

the

influence

regard

sufficiently

ions

in

about

term

With

should

the v a l u e

Fe 3+

of Fe 3+ ions. become

M g 2+

of the

quenched

of M g 2+ i o n s

to be

presumption

can

when

shifting

do n o t

temperature

/42/.

( 4 d lO)

positions

found

of

solutions

However

obtained

and

same

A contribution

replacing

increase

samples

q~ne c o n c e n t r a t i o n s

from

A-sites.

the

large

/40/.

/39/,

solid

of r e l a t i v e l y

simultaneous

8.400 ~ for

diluting Fe 3+

tendency

is c h a n g e d

/38/.

increase

vely

increased

structure

• - lattice

N i 2+

of

ions

the

the

size

positions into

the

C~stal chemist~ of magnetic oxides

4.2.3.

Substitu~on

of..trlvalent

cations,

Replacing

Cr 3+ ions in the ootahedral

positions

structure

and a tendency

ions

existing

according

appears

in Fe304

293

lowers

of Fe 3+ ions by AI 3+ or

the stability

of the inverse

to the r e d i s t r i b u t i o n

of iron

to the r e a c t i o n

and the mixed structures

of the formula

F e l3+ - ~ Fe~+ / F e l2+ - ~ Fe3+ l-x+6 Me~+/O 4 where Me 3+ = Cr 3+, AI3+~ Similar

behaviour

are formed /43/,

can be observed

/44/,

/45/.

in the system F e A 1 2 _ 2 x C r 2 x 0 4

/~6/,

where

reaction

Fe~+ + AI~ + = Fe~+ + AI~ + leads

to the f o r m a t i o n 2+ Fel_ 2

AI~+

as a consequence

(317

of the mixed structure 3+ /Al2(l_x)_ 2

2+ 3+ Fe 2 Cr2x/04

of the low p r e f e r e n t i a l

energy

of A13+ ions

to o o t a h e d r a l

positions. The simultaneous

influence

valency

among

series

exchange

of the tendency

the present

C o x F e 3 _ x O 4 solid s o l u t i o n

cations

to form a mixed have

of the inverse

structure

and the

to be c o n s i d e r e d

in the

Fe304

Co304

and n o r m a l

spi-

nels. The structure

It remains ximately

is controlled

in p r i n c i p l e

by two equilibria:

Fe~+ + Co~ + = Co~+ + Fe~ +

(327

Fe~ + + C°~ +

(33)

more

=

C°~ + + Fs~ +

or less inverse

up to x = lj where

F e 3 + / C o 2 + F e 3 + / 0 4 • Then in the range

may be d e s c r i b e d

the d i s t r i b u t i o n

of 1 < x < 2

is appro-

the structure

which

by the formula

3+ 3+ 2+ 3+ 3+ Co 2+ a Co b Fe l-a-b /Co l-a-b Co x-i Fe 2-x+a+b /0 4 is f o r m e d

because

distribution.

of a n e g l i g i b l e

Values

preference

of the exchange

enthalpy

of cations close

to a p a r t i c u l a r

to zero y i e l d e d

from

the

294

E. Pollert

experimentally the

determined

equilibrium

between

the presumption

concentration

of C o 3+

ly c o n v e r t e d H

The

to

= - 17.5

ex

observed

series~

ions

leads

evolution

content the

Fe

of

the normal

4.2.4.

Cu

it

the simplified

model

(a+b)(2-x+a+b) in (x-~-b)(i-a-b) /47/.

(above

However

x = 2)

indicates

influence

d%~dS] i o n s

holes

in

- ferrites exchange

of

in

the

of

(34)

when

a eritieal

structure

the value

of

the both

is

gradual

of

the

of

The

ease

cell volume

C o 2+ i o n s

and

it

in

the

but

the

of c o b a l t

electron ener6~ for

simultaneously

lattice

easily enlarged by 2+ Co lens are placed

is

the Coulomb

substitution

more the

end members

In particularly

the former

the unit

large

ones

Co304.

latter.

the

can be

octahedral structure

and valency

1 = R"~

tendency

as

reflects

the relatively

than

one

the decrease

tetrahedral

anions

this

using

F e 3+ i o n s :

is r e a c h e d

0 h and normal

of F e3 3+

to

and

k J m o l -I at x = 2 . 5 2 .

contribution

steric

of

ions

the normal

inverse

c o n f i g u r a t l"o n and

distributions

cobalt

1 /C°A/ /Fe~ +/ : RT -- in /COB//Fe ~+/

~ ex confirmed

cation

all

increases.

the

shifting

into

iron the

Because

of

oxygen

the A - s i t e s

and

is f a v o u r e d .

and derived as

in

solid

s~lution._SSSo

the previous

case

also

A tendency exists

to

the c a t i o n

in the CuxFe3_xO ~

system.

Hence

the

cation

CUA

distribution

+ Fe~ +

CU 2+

leading

to

the

+ Fe~+

general

+

2+

is

controlled

=

CU2+A + F e B 2+

=

Cu2+

by

the

(35)

+ FeZ +

formula

2+

3+

2+

~ 3+

CUaC~_aFel_b/CUx_bFel_x_a~el+a+b/O~ and

its

similar

Both at the

dependence to

transfer

(35)

temperatures

prevailing

ratures

the

the

temperature

~

can be

expressed

by

influence

the

an

expression

(34).

reactions,

high

on

reactions

reaction

436)

(1473

entropy cation

and

term

exohange~ (35)

is

simultaneously

K) w h e r e

the

distribution

contribution reaction still

possible.

to 436)

the is

Gibbs

inhibited

is

equilibrium

random

ener¢,~. whereas

stave

because At

low the

of tempe-

electron

Crystal chemistry of magnetic oxides

Consequently butions

by q u e n c h i n g

down

to the r o o m

295

temperature

nonequilibrium

distri-

/48/ C + F e 3 + i~ 2+ F 2+ F 3+ ~^ ub l_b/UUx_b el_x_ b el+2b/U 4 for

x <

l-b

and

+ 2+ 3+ 2+ 3+ CUl_xCUb_l+xFel_b/CUx_bFe2_x+b for

It

can

be

x >l-b

respectively

illustrated

by

authors

samples

with

yielded

the d i s t r i b u t i o n

which

This

the

exact

spinel

composition

to the f i r s t

(x=0.5)

of 1447

of ions

is,

however,

=

by an a n n e a l i n g

becomes

redox

reactions

like

solid

solutions

in the

/49/

and O . 5 < c < I /55/,

This

phenomenon copper

to a n o t h e r operative can

the

Jahn-Teller

their

other.

that of

by

presence

Consequently

regard

to

the

by

quenched

from

1523

K

distribution

unstable

given

and when

according

above

type

/53/°

annealed

below

to the r e a c t i o n

the

tem-

/54/:

/52/,

their

(37) high

valencies

contributes

temperature

where

are redistributed.

also

to the

composition

migration The

decompositions

ranges

of 0 . 2 <

interof s p i -

x < 0.5

/56/. for

the

iron

a small the

concentration effect,

be p r o v o k e d

as by

with

show

studied

F 3+ i^ el.51/u4,015

intermediate

trivalent

composition

A sufficient

(37)

is a b s e n t and

investigations the r e a l

CUo.52Fe2.4804.015

sufficiently

and

nel

spinel

investigations of the

CuFeO 2 + 2Fe203 at

noticeable

nal

valent

of the C u o . 5 F e 2 . 5 0 4

of the

K it d e c o m p o s e s

2CUo.5Fe2.504 conditioned

example

+ ~ 3+ i^ 2+ = 2+ Uo.24~eo.76/UUo.28eeo.21

corresponds

perature

arise.

/49-52/. The x - r a y a n d m a g n e t i z a t i o n

several

C

the

/

composition present.

part

of C u O

stable

their

spinel

of Cu 2+ ions

tetragonal distorion.

is s e p a r a t e d

(3d 9) i n

i n the

in tetrahedral

us n o t e

where

only

di-

that

the r e c e n t

from

CuFe204

and

is C u 0 . 9 6 F e 2 . 0 4 0 4 .

As f o l l o w s

presence

of the

Let

deformation

the d i s t r i b u t i o n extent

x = I~ C u F e 2 0 4

are

the

lattice

leads,

of the

lattice

due

from

the T a b l e

ootahedral

sites

(e/a<

of c a t i o n s

distortion

as

sites

l) a n d

act

is v e r y c a n be

IV

and

seen

Fig.

(c/a > l )

from

co7 it

as w e l l

against

important

however,

to the

each factor

the

Fig.

17

296

E. Pollert

where 1123

the K

dependences

are

of

the

transition

temperature

quenched

originally

from

/57/.

given

OD6

7OO

0.~

0.02

Loo,

2OO

1oo 200

Fig.

17.

~100

/,00

dependences

and

tetragonality

CuFe204

of

the

concentration

From

this

x.

0 ~x

< 0.3

due

to

of

point

illustrative with

annealing

on B - s i t e s ~

to a n i n c r e a s e

The

to

here has

the

effect

700

of

~0

the on

quenched

900

1000

transition

the

the

annealing)

in

leads

to an i n c r e a s e

of

/57/.

temperature as

c a n be

seen

from

the T a b l e

the

study

the

occupation

a tetragonal

prevailing

of C u 2+

ions

structure

effect

nearly

iron

ions

The Ti t+

reason pairs

substitution

all

Cu 2+

distortion

is

Cu 2+

due

ions

to

with

in A-sites

ions

were

present

influenced

by

that

B-sites)

kind

of

also varies

o/a > 1 in the r a n g e

in the r a n g e

in

the

is

by C u 2+ i o n s

of C u 2+ in B - s i t e s

of CuFe2_2xZnxTix04 and CuFe2_2xGax04 2+ Cu A < 0 . 0 5 i n s t u d i e d samples was ensured

of

the

and

solutions

of A a n d B - s i t e s

solid

e.

VII

of C u F e 2 _ x C r x O 4 s o l i d

by

i.

temperature

after

tion tent

temperature

annealing

Comparison of

~IOOK

T

distortion.

of v i e w

series

due

the

the

/57/;

600

The

(samples

Lowering

500

and with

i

of 1.4 < x ~ 2 .

solutions

slow

(concentra-

cooling

indicates

the

of

o/a<

ions

of

that

samples the

substituted

ex-

for

/58/.

is

in

causes of

the more Ga 3+.

Coulomb rapid

energy

contribution.

decrease

Consequently

of the

the

spinel

Substitution Coulomb structure

energy is

of than

Zn 2+ does

stabilized

and the by

Crystal chemistry of magnetic oxides

this energy g a i n and the c o o p e r a t i v e duced.

Due to that the c r i t i c a l

297

Jab_n-Teller d i s t o r t i o n

concentrations

is not more in-

are x = 0.08 in the f o r m e r

s y s t e m w h i l e in the latter x = 0.7. T a b l e VIII. V a l u e s

of q u e n c h i n g

distribution

Quenching

temperature

temperature

%

and c a t i o n

in copper f e r r i t e +)

/K/

Cation distribution 3+

2+

3+

2+

slowly c o o l e d

Feo.91Cuo.o9/Fel.o9Cuo.91/O 4

873

Fe 3+ Cu 2+ /F 3+ C 2+ .~ 0.76 0.24 / ei.24 u 0 . 7 6 / u 4

1073

F 3+

1173

Fe~68Cu~32/Fe~32Cu~68/O 4

+)S.A.

_ 2+

i~ 3+

~ 2+

I~

eo.72UUo.28/rel.28UUo.72/u 4

Patil,

I n d i a n J. Pure Appl.

Phys.

2~i, 182 (1983)

4.3. M a n g a n i t e s

The most i m p o r t a n t of the cubic sufficient

property

the lattice,

distribution

of their v a l e n c i e s

spinel g r o u p is the t e t r a g o n a l d i s t o r t i o n

to f a c i l i t a t e

Jahn-Teller

of the d i s t o r t i o n

effect

of c a t i o n s

between

of M n 3+ ions at

is s i m u l t a n e o u s l y

like k i n d of cations p r e s e n t

and c l u s t e r i n g

4.3.1. _Hausmannite. spinel

this

concentration.Extension

f l u e n c e d by f u r t h e r factors~

but

of

lattice due to c o o p e r a t i v e

in-

simultaneously

the s u b l s t t i c e s ~

in

distribution

tendency.

Its s t r u c t u r e

belongs

c o m p a r i s o n w i t h cubic

space g r o u p O~ (Fd3m) is used.

to the s p a c e g r o u p D 419 h

spinels u s u a l l y

Lattice parameters

(z ~l/amd)

description

in the

are t h e n c o n v e r t e d

by the c o r r e s p o n d i n g manner:

a

sp

=

The d i s t r i b u t i o n configuration. covalent

a.

~7

o

sp

--

o

of c a t i o n s M n 2+ / M n 3+ 2 /04 is d e t e r m i n e d by their e l e c t r o n

Ions M n 2+ (d 5) occupy w i t h r e g a r d

to the p o s s i b i l i t y

of the

b o n d t e t r a h e d r a l p o s i t i o n s w h i l e M n 3+ (d 4) ions are s t a b i l i z e d

ootahedral positions distortion

of the lattice

(see Fig.

Mn304 was s t u d i e d by s e v e r a l a u t h o r s the t r a n s i t i o n

in

by the s p l i t t i n g

of e g level l e a d i n g to the t e t r a g o n a l 16). T e t r a g o n a l - cubic t r a n s i t i o n in /59/,

/60/, /61/, /62/

and

values

t e m p e r a t u r e T t = 1445 K and the t r a n s i t i o n e n t h a l p y

of

change

298

E. Pollert

& H t = 18.81 k J /63/ are r e p o r t e d . T a b l e IX. T e t r a g o n a l

deformation

of some m a n g a n i t e s

Tempeq ~ a n s - rature Spinel

Lattice parameters a/~/ 0/~/ e/a

Distribution

irish

of

tempe-

rature

l~ef .

prepsration

Tt/~/

T/~/

Mn304

Mn2+/Mn~+/

8.149

9.456

1.16

1445

1520

/60/

ZnMn204

Zn2+/Mn~+/

8.10

9.25

1.14

1923

1173

/65/

Co~n2%

co~i Mn2%~ 9+.,3+ lWO ~m2_

8.168

8.958 1.097

1523

/65/

8.197

9.041 i.iii

1273

8.096

9.133

1.128

1079

1.09

1219

+

,. 3 +

/^

2+

/

,

3+,

4+

~u0.761~m0.24/~u0.24~n

ZnOrMn04

Zn2+/CrS+Mng+/

8.25

8.62

1.04

/66/

ZnGaMn04

Zn2+/Gag+Mn3+/

8.23

8.64

1.05

/66/

LiMa004

Li+/Mn4+MnS+/

8.25

I n fact

the c o e x i s t e n c e

range tion

region

18). The course

The latter

off the g r o w t h

or d e c r e a s e

/64/.

4.3.2.

of v a r i o u s

IX.

Substitution

manifest

depends

sites

the r e s u l t i n g t h a n those tron

cations

distortion

of ions p r e s e n t

of the s p i n e l s t r u c t u r e

simultaneous-

Examples

condition,

of spinels

listed in Table

of ZnMn204

It is c a u s e d by the d i f f e r e n c e in t e t r a h e d r a l due to s t r o n g e r

sites.

distortion

the t e t r a h e d r a l

of the same e o n o e n t r a t i o n temperature

and

of / M n 3 + / B

= 1

are lower in the elec-

An increase

covalent

i. e.

on the d i r e e -

tetragonal into

the tran-

The c o n t i n u a t i -

in the d e p e n d e n c e

substituted

and t r a n s i t i o n

in the

the t r a n s f o r m a -

acts against

of the e q u i l i b r i u m

of the m a c r o s c o p i c

of MI~ROQ. I n spite

of pure h a u s m a n n i t e .

structure

bility

cations.

that the e x t e n s i o n

on the k i n d of others

octahedral

change

phases

term E s t r a i n s (which is in fact

contribution

of the t e m p e r a t u r e

tion of the p r o c e s s

for

is c o n t r o l l e d

of e m e r g i n g c r y s t a l domains.

on of the t r a n s f o r m a t i o n r e q u i r e s an i n c r e a s e

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

of the t r a n s i t i o n

of Eel and of the s t r a i n s

of the p V c o n t r i b u t i o n ) .

s i t i o n and eutts

/66/

of the low and h i g h - t e m p e r a t u r e

of 50 K and a large h y s t e r e s i s (see Fig.

ly by c o n t r i b u t i o n part

Mn0.76

/65/

CuMn204

of the sta-

b o n d at Z n 2 + ( d 10)

Crystal chemistry of magnetic oxides

r

1-

[

-o-,r,.c.~

r

-

, ~ I ,

r

,

,

,

i

,

,

-T--I

~-

T--~T

~

299

r

T

r

S

q

,

q

-

r

\o

0.8

0.6

X= . !

0.4

0.2

I

0

6~.o' h ,

'

' eeo ',

T(K)

Fig.

18. The t e m p e r a t u r e - to - cubic gions

hysteresis

t r a n s i t i o n and the two p h a s e r e -

in the M n x C r 3 _ x O 4 system.

than at M n 2 + ( d 5) leads to the w e a k e n i n g ions /67/.

Lowering

f r o m the d e p e n d e n c e

exists

of the d i s t o r t i o n effect

of the t e t r a g o n a l d i s t o r t i o n at C o M n 2 0 4 of the c/a on the t e m p e r a t u r e

ted w i t h the r e d i s t r i b u t i o n re. C o n s e q u e n t l y

of the t e t r a g o n a l

of v a l e n c i e s

concentration

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

and f o r m a t i o n

of / M n 3 + / B

of the c o n f i g u r a t i o n

t u t i o n in o c t a h e d r a l p o s i t i o n s coordination macroscopic

is d e c r e a s e d .

octahedral distortion

not s u f f i c i e n t

of the outer e l e c t r o n s

Critical

effect

is lower.

Concentration

for the d e f o r m a t i o n

of / M n 3 + / B

of M n 3+ ions g i v i n g rise

solid solutions,

the t e t r a g o n a l

l i s t e d in the T a b l e X, r e f l e c t in the s p i n e l lattice

of the type M e / M n 2 _ x A l x / O 4

by Zn 2+ and Cd 2+ ions r e s p e c t i v e l y l e a d s t o value because

covalent

bonds

of d lO ions in t e t r a h e d r a l

Overmore

ses a n i n c r e a s e

of e l a s t i c forces w h i c h have

distortion

similarly Typical

of

as the

examples of M n 2+

/Mn3+/ c r i t i c a l

sites act against

in the latter case the large size of Cd 2+ ions c a u -

S n 4+ ions s t a b i l i z e inhibit

is

a g a i n the p r o -

/68/ where replacing

the i n c r e a s e

the d i s t o r t i o n .

consequently

= 0.5 h o w e v e r

/66/.

of c/a and T t do in the case of simple spinels.

are s o l i d s o l u t i o n s

of the

at L i M n 2 0 4 w h e r e E e l c o n t r i b u t i o n is lo-

of the other cations p r e s e n t

magnitudes

at the s u b s t i -

cubic s y m m e t r y

and in c o m p a r i s o n w i t h G a 3 + ( d 5) ions the r e s u l t i n g

concentrations

in m a n g a n i t e

and

Similar

appliee

too. C r 3 + ( d 3) s t a b i l i z e

w e r e d by the o r d e r i n g of M n 3+ and M n 4+ ions in B - s i t e s

valency

connec-

of the m i x e d s t r u c t u -

at C u Y m 2 0 4 . / 6 5 / .

Influence

perties

of M n 3+

is as f o l l o w s

octahedra

to be overcome.

in the systems

the m a c r o s c o p i c

distortion

Similarly high

containing

/69/.

tin ions

300

E. P o l l e r t

Table

X.

Some

examples

of m a n g a n i t e s

solid

solutions

Critical System

Distribution

of c a t i o n s

tion 3+

/Mn M n Cr~ x

Mn2+/Mn~lCr~x

0,.

3-x

M

MnxFe3_xO 4

2+

Mn 2_xSnl_x04

3+..

~

2+

n.±-y re y / M n

Mn2+

MnxC°3_xO 4

~

/ 3+

1~e~3O+- ~~y - x ~re y2 + . / x+y-±

~..

~

3+

~

Ref.

concentra-

2+

~

/Berit

0.4

/71/

0.475

/71/

3+/

/93,94/

uo /~m uo uo / 0.56-0.65 l-y y-2 x+y-l-2 3-2y-x+2 y ~m2+/. 2+ . 3+~ 4+ /~tnl_xMn2x~nl_ x 0.5

/69/

M 2+~

--3+/

0.61

/68/

MgxZnl_xMn2_ 2xA12x04

2+ 2+ 3+ 3+ Mg x Znl_x/Mn2_2xAl2x /

0.68

/68/

M g x C d l _ x M n 2_ 2x A 1 2 x 0 4

~ 2+~2+ /. 3~ ..3+~ gx WUl--x/Mn2--2X~±2X /

0.72

/68/

MgxMn3_3xA12x04

In Mn-Fe

results which

that w h e n

The

solid

~Cr 3+)

solutions

and

ootahedral positions

ions

the

in p r i n c i p l e

spinels.

of t e t r a g o n a l Let

in this r e g i o n tetragonally

of the

and d i s t r i b u -

existing

in M n - F e

gap region.

lying

to the r e m a r k a b l e sites.

Further

resulting

from

of the M n ~ + i o n s

and

to the

in octahedral

i n MalxFe3_xO 4 system, character

preference

due their

electron

This and

us note~

deformed

ten-

cubic

however~

are a n n e a l e d phases

In contrary

at may

be

by d i f f u s i o n

Fe 3+ ions

of the d i s t r i b u t i o n

the

3d 3,

separation

are more

mobile

to occupy

clusters

during

to their

ions the

the c l u s t e r i n g

the

gap r e g i o n .

due

of Jahn-

in o c t a h e d r a l

Created

states

study

of c h r o m i u m

of Cr 3+ ions

restrained.

the

the m a c r o s c o p i c

state

configuration,

metastable

to that

for

object and

of M n 3+ and Cr 3+ ions

in the m i s c i b i l i t y

of c a t i o n s

because

valency

to the s t a b i l i t y

is c o n s i d e r a b l y

phases

a suitable

of M n 3+ ions

to the f i x e d

intermediate

tetragonal

sites.

represent

concentration

with regard

the r e d i s t r i b u t i o n

random

of v a l e n c i e s

separation

metastable

MnxCr3_x04

between

correspond

of c u b i c der

composition

temperature

distortion

tendency

to the

influenoies

of M n 3+ ions namely

in the m i s c i b i l i t y

with

high

form

important

are v a r i a b i l i t y tendency

to be c o n s i d e r e d

in its f i n a l coexist

the most

by q u e n c h i n g .

the r e l a t i o n -Teller

clustering

have

samples

sufficiently obtained

systems

distortion

The

in a l l m a n g a n i t e s

phases

spinel

of t e t r a g o n a l

of c a t i o n s .

denoy

~.. 3+

gx ~nl-x/inn2-2xA±2x /

and M m - C o

"onset" tion

2+

of Mn 3+

separation

Cr 3+ ions h i n -

high

is v e r y

stability fast

e. g.

than Cr 3+ ones. T h e

of M n 3+ and Cr 3+ on B - s i t e s

oorrespon-

Crystal chemistry of magnetic oxides

ding

to the h i g h

the c o o l i n g existing several sition

and

temperature to a t t a i n

in the m i s c i b i l i t y hundred

hours

temperature

conditions

remains

the s e p a r a t i o n gap region

/70/.

I n spite

301

consequently

of t e t r a g o n a l

(see Fig.

19) r e q u i r e s

of the d i s t i n c t

on the c o m p o s i t i o n

was

unchanged

a n d cubic

co-

annealing

for

dependence

determined

after

phases

of the t r a n -

by D T A / 7 1 /

the r e a l

1600

T[KI 1600

Cr~O**C

c

/Cr203

T*C

r300



o~



s° 10(

Fig.

19.

Cr~O)

25

Phase

50 mnmm~i= [mo,.I~

diagram

B - bixbyite

course

of the

coexistence of about

transition

of b o t h

50 E.

The

sufficiently

dilute

see Fig.

/72/,

18

In contrary nel

exhibit

their

and

on B - s i t e s

exists

equilibria

similar

Experimentally

to the

thermodynamic

were

proposed:

mutual

series

in

spinel,

as in the case phases

dissapears

interactions

a tendency transfer

solution

to the e q u a t i o n s

the d i s t r i b u t i o n

using

arise

similarly

electron

in solid

authors

compounds

system

of p u r e

hausma~ite

i n the t e m p e r a t u r e when

region

the M ~ 3+ ions b e c o m e

are w e a k e n e d

(x = 2.15),

/73/.

veral

rich

- Cr203

T - tetragonal

temperature

of h y s t e r e s i s

to the c h r o m i t e

structure

Problems

and

~ln z O)

type phase.

low a n d h i g h effect

spinel~

i

75

of the M n 2 0 3

air. C - c u b i c

s °J~

and various model

in p a r t i c u l a r (x ~ 1), w h e r e

for

(32)

/e.

above

manganese

of m i x e d

and iron

M n x F e 3 _ x O 4. C o n s e q u e n t l y

and

of c a t i o n s

methods given

series

to the f o r m a t i o n

between

(33) h a v e

and

two

to be c o n s i d e r e d .

and valencies

g. 7 4 - 8 4 /

spi-

ions

was

it was

studied

also

by

se-

calculated

/85/°

stoiohiometric

two l i m i t i n g

.. 2+ ~ 3+... 2+.. 3+ _ 3+ i^ i. M S _ re /MS MS ~e^ iu~ ±-y y y x-± j-y-x

MD-Fe204

models

and

the m a n g a n e s e

of the i o n i c

distribution

302

E. Pollert

2+ 3+ 3+ 3+ 2+ 2. Mnl Fe /Mn Fe ~ Fe /0, ±-y y -- x+y-i 3-~y-x y

The

first

while

model

the

tion

of

is

second

the

supported

one by

second

experiments

/86/. among

neously

electron

With

regard

and

to

influence

compositions or

slow

The

ooou_rence

pendences Fig.

can

support

to e x p l a i n

20.

of

the

o / a vs

Existence

the

the

the

"cubic"

the

central

of Fe 3+ i o n s

properties.

It

~ modifica-

of

the

that

easily can

and

effect

be

ions.

already

are weaker the

other

MnxFe3_x04

and variations

and

This

o

1.10

105

100 --

15

Fig.

20.

Dependence series

25

21]

of e/a

(Polle~t,

results),

x

on c o m p o s i t i o n Holba,

Nev~iva,

0 - M n x C r 3_xO 4 s e r i e s

30

Q - MnxFe3_xO 4 unpublished /71/.

de-

see

values

/

115

idea

in the

c

at

their

systems,

of o/a

/87/. than

hand

in contact, ions.

for

Annealing

microdomains

of / M ~ + / e r i t

in M n x C r 3 _ x O 4 a n d

Mn2FeO 4 /88/

On

are

the

in o h r o m l t e s

observed

of d i s t o r t i n g

in the v a l u e s

to

simulta-

of Cr 3+ i o n s , than

tetragonal

clusters

of

ion.

of M n 3+ i o n s

distorting

where

kind

belonging

c o n c e n t r a t i o n of M n ~ + i o n s . clusters

/78/,

both

electron

than

more

the

M n 3+ i o n s

M n 3+ c e n t r a l

in f e r r i t e s

cooperative

composition of

model

distributed

difference

Recently

improved

the f o r m a t i o n

of M n 3+ ions

/84/.

explain

oritieal to

/83/,

measurements

could

with

their

spectra

which

of i s o l a t e d

of r a n d o m l y

concentrations

allows

here

of N M B

surrounding

formed

the

interactions

interactions high

near

leads

the

mobility

are

significantly lying

coolin~

mutual

to

is b o u n d

the h i g h e r

M~ssbauer

proposed

Fe ~+ i o n s

of M n ~ + ions

clusters

the

results

was

According

"Fe 2+'' j u m p s this

the

model

by

with

Crystal c h e m i s t r y o f m a g n e t i c o x i d e s

the

annealing

phases

are

Let

note

us

/89/

have

separated

that

the

and

the

samples

and

quenching

crepaneies

Likewise spinel

among

as

and

to

the

g. f r o m

this

equations

system

to a h i g h

/93/. ned

From

is

and

(33)

/95/.

Mutual and

good

experimental

Table

it is

the

XI.

The

origin

annealing

of

the

dis-

two

of i n d i v i d u a l

independent On the the

distribution

of

other

hand

cations similar

as f o l l o w s

effect

of c a t i o n s

corresponding

preserved

to c o m p a r e

the u s e

equilibria

clustering

easily

valencies

of m i x e d

by

quenching

experimentally

/94/ with

those

the

described

of the p r e f e r e n t i a l

energies

in

determicalculated

thermodynamic yielded

from

/74/.

Comparison

of c a l c u l a t e d

and

determined

distributions

of c a t i o n s

in the

temperature

1473

MnxCo3_x04

at

the

experimentally

oalo.

2+ 2+ 3+ 2+ 3+ Mno.68C°0.28C°0.04/C°O.08Mnl.84/

exp.

i,n n 2 +

K

n 2 + 0.63U°O.29~no.o8/U°o.o8Mnl.92 / ~ 2+

. 3+

/~ 2+

~ 3+

~ 2+ .. 3+ /~ 2+ ~ 3+ 0.28U°O.56~no.16/u°0.16~mnl.84

/

/

oalo.

nO.43U°O.52U°O.O5/u°o.osU°O.l~nl.85/

exp.

no.18U°O.82/U°o.18U°O.42~nl.4/

oale.

2+

ku2+

~ 2+

~

2+

- 3+ ~ 2+

~

~ 3+

2+

. 3+

~ 3+

~

i

3+

/

O.iu°O.2U°O.7/U°O.20U°O.35~nl.45 /

spinels

fundamental

formula

the v a l e n c i e s

k

2.28

Vanadium

the

~ustifies

cubic

to p r e p a r e by

formation

exp.

2.63

4.4.

of the

composition

their

employment

system

1.58

of

c a n be m o r e

and

agreement

data

and

difficult

the

and

/90/.

distribution

is p r o b a b l y

a tendency

interesting

of c a t i o n s

supports

vs

equilibrium

reason

it a l s o

cation

c a n be w r i t t e n .

of o/a

tetragonal

gap region

authors.

Consequently

pronounced

temperature

model the

less

this

example

of the v a r i a t i o n

(32)

distributions

This

of v a r i o u s

exists.

Ultimate~-

makes

equilibrium

/91/, /92/.

the d e p e n d e n c e

too.

the m i s c i b i l i t y

tendency

the

in the f o r e g o i n g

in MnxCO3_xO 4 system

e.

with

the r e s u l t s

structure

origin in

clustering

the M n - f e r r i t e subsequent

same

coexist

303

MeV204~

group

are

where

Me

spinels = Cd,

Zn,

of

the

Mg~

trivalent

Co~

Mn,

vanadium

Fe w i t h

of

the

the n o r m a l

general structure.

304

E. Pollert

0.394+-

C~:y

0392 0.390

i ct~

OCo

8<.

Fi~.

21.

Relation oxygen

A

linear

(Fig. ons

relation

21)

is

an

present

a~ainst radii

the are in

that

the

at

verse have

equation

such

to

the

and

solubility nal

The of

effects

lowest Cd 2+

are

=

one

notable as

there

we

the

oxygen

parameters

of

sizes

the

supports

~ and

tetrahedral V in

and

/!)6/.

coordinated

most

our cations

u

of

cati-

~bjections with

small

inere~i~se s i m u l t a -

site

[ncz'eases w h i l e

- 0 = 2.024

~ /96/.

The

in-

the

M e ,V04 s p i n e J s but they 2 because of t:he i e n d e n c y oi

cases

+ V 5+

('~5)

existence

oJ-" the

re~ions

vary

for

each

individual

have

to b e

of x

value

stron~ the

range

are

and

radii,

expected

in

limits

have

pV

the

the

preference

ted

possibly

and

influence

constant~

from

preference

tly

~t

see

simultaneously

Strong

term

can

causes

homogeneity

the

lar~er

hole

meanin~

V ~+

the

As

ions,

property

be

constants

of

remains

constants spinels

disproportionation:

restricts

M e 2 V 0 %.

with

the

site

should

2V ~+

which

that

lattice MeV204

tetrahedrally

cations

a way

lattice

sterie

If

8,6a[A] 87

the at

example

the

(29). by

hypothetical

ions

their

on

octahedral

structure only

V~+

between

replaced

neously

between parameter

illustrative

in A-sites

8.5

taken

in

cadmium

preference

placed

spinel

of

Z n 2+ i o n s Znl+xV2_x0~

to

any

additional

solutions

the v a l u e s

systems

series

to A - s i t e s of

in both

in

solid

XIX,

and

between

of

x,

MeV>O~12

[. e.

consequently

the

additio-

aeeeun¢.

destabilization A

for

and

and

previously effects

the

and

and

results

from

laramie i o n i c

spinel

lattice

t~

properties

radii. when

]~he l~=~ttar

c~dmium

ions

B-sites.

A-sites

solid

position

demonstrated no

into

Table

decre;~ses

the

;~lso

solutions.

Magnesium

tend

rather

with the

to be some limit

spinel od

the

exlenl

<~I t h e

i,~ns e x h i b i t

randomly systems. existence

no

distribuConsequenel" s p i n e l

C~stal chemist~ of magnetic oxides

solid s o l u t i o n in this series ions a c c o r d i n g

The v a l u e s



as far as at Fe2V04

of V 4+

:

(36)

= (Mg2V04)x_4-MgV204+Mg3(V04) 2

of x i n c r e a s e for Mn, Co and Fe ions b e c a u s e

Me2 + + v

lattice

is only g i v e n by the d i s p r o p o r t i o n a t i o n

to the r e a c t i o n

(2x-4)MgO+xVO2

305

:

3++v

(37)



(x=l) no t e t r a v a l e n t

and the d i s t r i b u t i o n

of the r e a c t i o n

of cations

vanadium

ions are p r e s e n t

in the

g i v e n by the f o r m u l a

F 2+ ~ 3+ ._ 2+ ~ 3+ ..3+.e0.399e0.61/~e0.61reo.39 v /u 4 is r e a c h e d /I00/,

/lO1/,

/i02/.

Table XII. H o m o g e n e i t y

range

solid solutions

in M e l + x V 2 _ x O 4 s p i n e l

/97/, /98/, /99/.

System

4.5.

x

Cdl+xV2_x04

0.025

Znl+xV2_xO 4

0.35

Mgl+xV2_xO 4

0.65

Mnl+xV2_x04

0.69

COl+xV2_x04

0.9

Fel+xV2_x04

i

I n d i u m and tin spinels

With regard

to the e l e c t r o n c o n f i g u r a t i o n 4d I0 of b o t h In 3+ and S n 4+ ions

respectively

it should be p o s s i b l e

the t e t r a h e d r a l

It appears

to assume p r e f e r e n c e

j u s t i f i e d for the m i x e d oxides

Me 2+ are M g 2+, Ni 2+ and Me 3+ are A13+, A-sites

are formed.

preference

of the f o r m u l a M e 2 + M e 3 + I n 3 + 0 4

Ga 3+, 0r3+.

if

T ~ e n spinels w i t h I n 3+ in

On the other h a n d w h e n Me 2+ are ions w i t h a s i g n i f i c a n t

for t e t r a h e d r a l

rhombohedral

of these ions for

sites.

structure

sites,

like M n 2+, Zn 2+, Cd ~+, m i x e d oxides w i t h

are f o r m e d /103/.

306

E. Pollert

]'he

solid

solutions

appreciable of

the

former

quenched the

Fe2+Xn3+Fe]+x

tendency series

from

where

enerf>ies other

iilJ['luenoed

by

Lho

tetldeTloy

relati-¢ely

.l_[71r{>e

but

]~]le

ei'i'eot the

i4.0.

An

have

the

of

strong,,

J onto

~i~h

outslandin{,,

property

siinult~neously

presenl

~ln

effort

~o

crystal

tile

and

order ]s

ordered

[~nd

nol

order

]'here

~

find by

~hvce i:

j [

Below

is

(lt'[

I (~ hi!

1_1$ l ] o i { ,

{)coup) + breJ'(.reill

])rl)lc]eulloe(l

the

_l.r/3~ si,,lt.

(+]lt;-)4

ih(,

.l'{}i'

i !ills

-

:is

;~n~t

I
Ih~,;[l'

~ ]l(,l,t,

l o ,, .

~i,I,

(hi.

I (} 13~,

ions

"

,>ill{~r

hi]

J;l]]],

t) eas(,

s;,mp]<'s

ot~D,~Jd~'r~'cl {>1

i]/;il

f]'~,iil

ltae

i n

YI>{)III o l ] e

ili()ri9

Spill~'ls

:iS

t~ele]~[tilt

,)~

lh('

r,l>i]ily

stlbl;llfioo.

con[ribu

i J on

suffioJ~,nl

life

o}]ll b e its

,

tl-sJ

I ~ ,l'cl(!l

I (..~

ltii:

[[[.~ r(,tsoll

i {~

t h(

Li'c~'

d.it'lor(~noeb

<,rderinM

]flus

[['orl]l~il

ordert'd

phrases


is

, 1()~)/

"

O ; t l [~11~"

i~I)+)¥~, a ] ]

("~/ t t ~ : ~ l ~'5

is

cl{~g,r]y

I r~i i:ocl b y

ioli

tl~,

i:ypts I es

l~';~s

][ts

n{ll

o~/li

St,

i ltc

i~

~i

I hr,

v~lolieie~-

rind

rc, iril o
I hl ~ s p i n e ! J~

tlssillllod

si~,1o~

:in

:

kl, l/

I]-]V

I iI];i f l y

|)(li~l

Ot)lllp]_~.i e l y

referred

1020

1o

] : I

lt~

k

beeolnes

,,J

~.

l,iNi;/(!sl

inx, e~'~{

]]-iii

~,

~ht~

i lli:~ ~ ; * ] c n [ : ! <~el ~1~

i .

~,.

~lJisltJs

i nv{~r:~c~

]_t

lJ~)lh

Sl~ in+~Ls

(i~

en~niiomol,

oF

ph

~ind

P~{I]I]2

lh~,

]ililJtlin

ill<]s(,

There

{~xi.s] s

e{){lsJ s {

kb

;~box:t,

i olrrlhedr~ll

;i llc;ly5

spin~.]s

5p[l]{'.].s~

It'(till

disf~rder{~d

f~[ioh

~he

iirl

~)3

lil]lium

the

e~n

be

~nd

oc[
/,10S/ . ]'he

]lit,ill

i,,l],,~]

dex, e ] { ) p m e n l

It)'7()

I{

~hro(}

i,f i +

l]o~:ll'< ,~, I

dl]0o,

it-ell

the oi

I>til

i';ll]~,o

(,J

subl;lJ

i~2tll;,l'i~

:,i

.l i i h i l l l n

~t s ] l t ) r l

three

l)y

[),,l'l iht

7'~r(/tl][i

ohllr~',>[? LllXS{iri(irloo

ill

:

I:

I

ill

\-.~ i i l's .

One

°

[etr;71hedr~t]

{.'ener~tod

<~rdered

lilt,

)

r~tlld()lll.

J oils

sequences

~ire

in

is

;[1n] l + ] ] i o i ]

{is

!~rdel'illT,,

~d

~iIi~

struot'dr('

o o o l ' d in(7 t e d

directions i:mre

bonds

I [1(~)

by

M c • + / ' L i ( ) .+s L . ( ~"I] . 35+/ ( ~ t

lTe~l-t).

hedr~lly

its

l]-sJ

{]13 [ : t r r ~ ] c l 6 " e l l l o n l

;~nd

oovrllei]i

ho~ovei',

i tel'I/ • (JilllSO(illol]i i h-

beh~,viour

1~> A - s L i t ' s )

ColllOlllb

in

basic

'i ill

~lttelll:ion

:

lit

only

dJ soldered

forinul~

[Me ~+

}l~iVO

The

,

[cul~r]y

.

5pooiaJt'rll

i ons

3+

pari

v;,ndoill

(!%tel]

L$(}lile

ly

l~Ilis

e>xists l
~ll~e

B-sites

in

nearly

]3).

\s{i].c?lle~,"

{hi,

l]le

slab]l]

i oo.

spinel~

cd'

oonditiened

the

difference

hedral

o1'

is

c~,tions.

respective

Consequently oy

is

on

oxhibil

']'h~l

e~i{ L{)ns

in

iilinimize ] t

J'ol'ill

i s

± n x~" t~e,~_~{t~l_,

eciiJens

l!'J{,,.

s(.i'2[os

ordered

i bucJ

present

hi{Th

ch{ir{','l-!

be

I (, b e

prei'eI'one<'

Fe > Co S n O, 2-x ] +x x q

Spinels

~he

to

~lild

tr

found

[compare

size

;~lld

struel:ures.

dis

was

of

the

t'>er

2-x0'q mixed

the

K

te

in

each

form

I_510-1550

preference

close

to

I ')i]~

~

i
tie{~

i.(,ili(iiit~ ~ ['(t ,1,

[]:iU,.

otlbic

sp;tc(~

,>rdtn:"

i~

~,,,(,1;l,-

I{' illYt,l~b( l(,ii]

i z{'{t

I1(' [ { ~ J l b < l t l ] ;]lit]

J(),7

Ih('

l(,l>l'l

'lll('

(io I < -

I , I. 4

i O]/

.

:+')~

~lild < l ~ ( ) ~

lil(~ s l r u o -

,,,]'{} |~ P~I ~[~i! <>J'

e<~itri~'et(~{l ~

th

i he

Crystal chemistry of magnetic oxides

formation attained

of a n t i p h a s e when

only

domains

a single

22. O r d e r i n g

Fig.

tice

Spinels A13+

also

Due

to

the

crystal

their

Cd 2+ the On

electron field

energy

Coulomb those

the ions.

other

appears

one

is

of

the

hand

because

the

when

state

a redistribution

Li + a n d

the like

(space

complete

F~3m)

The

M n 3+ i o n s

ted

already

at

have

its with

in

ordering

e.

a large

are not

by

g.

by

the From

of Zn 2+ a n d and

is favou_~able. ootahedral

sites~

the

That

is

ordered.

the

dis-

ease

ions

On the

leads

in A - s i t e s

site

order

are 0.25

the B - s i t e s ill

stabilized

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

decrease

ootahedral

Me 3+ i o n s

the

Ga 3+ or

Fe 3+ - 3d5).

case

contribution

ions

of i r o n i o n s

Lio.sFeo.5/Cr2/O 4 where

group

formation

replacement

the

is h i n d e r e d .

limit

hand

- 3d I0,

concentrations

B-site

nels

is

are not

critical

their

that

(Ga 3+

the

by

is d e t e r m i n e d

of cations

where

above

in

is

/llO/.

sublat-

replaced

cations

lattice

than

energy

metal

of Cr 3+ a n d R h 3+ i o n s and

these

producting

introduced

ootahedral

order

/109/,

/iii/.

in the

significant

transition

are

all

Coulomb

the p e r f e c t crystal

or c o m p l e t e l y

contributions

less

ordered

energy

i n the

behaviour

position

their

and

in the

ferrite.

are partially

configuration

and

types)

present

lithium

a similar

Consequently

stabilization

the

and o o v a l e n e y

latter

formation the

exhibit

is

of c a t i o n s

of

iron ions

in which

ions

(8 p o s s i b l e

domain

307

per

other

to the

spi-

can arise

/66/.

a special

concentration

of M n 3+ c l u s t e r s

position 0.125

/112/

ions

per

(see manganites)

because

the

ordering

B-site.

The

reason

which

oposes

the

is

is p r e v e n in

the

ordering.

When

308

E. Pollert

the

concentration

Lio.5MnxFe2.5-x tetragonally can

be

of M n ] +

O'4~ e x c e e d s

distorted.

explained

sufficienl

by

the

contact

consequent]y

The

ordering in B-sites +, 2+ . ~ + ~ Li Me0.D~sel. SU~ divalenJ

Li/Coo.sMnl.5/OzI. from

the

for

The

fore~oin£~

reasons

or

ions

Let

The

note

of by

Lio.5Fe2.50~+ can

be

the the

short

rankle

order

the the

Jahn-Tel~(u

tetravalent

e.

of

order in

different properties

i:i

solutions

the

by

where

the

i: ~ i n

radii

applies

small

size

the

order

natin6

i:i

the

is

formed.

(00])

planes

pectively

and

Immb.

arran~e'ment

to

The

a more

between the

in

rows

term

~Jlh pV.

the
the
of

exists

only

The

nol

and , ,

V 5+

/ii!I/.

placed

of

~O ~ x --" ] ~)

is

is

lhe

s u b l a ! i -, e:

for

in

On

the

of 5 b ~>+ i o n s occupied can

eatior~s

be

th(

hand

Li + i o n s

of

their

opt-realization Couloinb

is

then

directions <011>

and

the

formation

sequentially <0~i>

in

the size oJ

B-sties

rows

occupied

directions

of by

and

by

alter-

ions

res-

space

{',~oup

{,,ires r i s e

the

conlribution of

spi-

tetrahed-

si~'nificantly

5 b 5+

by

only

the

o[' x /6()/,

th~

effectuated

Li + and

described

;~nd

O.'I a n d

LiMe~'*Me)+O,l

other

is

I~± "+

~<

valtles

occupy

allowi11(~ a n to

O<

only

by

beeause

by

Yor

vt>ry I o ~

ions

r~sp(,ctJ%ely.

created

found

tot'~eiher w i t h

phase

Nb 5+

result

i,~ ~is<>

~n(i

occupancy

like~ise

ihe

orderin~

structure regard

the

Li'l'J, Oq

l]-sites phase

exists

ardered the

[he

spinel

of B - s u b l a t t i c e

~risinc,

complicated

cations

steric

sites and

the

il

are

The

-

formu]~

~ It+ ']+ ~Inx F e l+. ~/O'I %

order

orderin G

~)n

F el. [~+5 - x T i x!I+/'()~I a n d

ordered

cations

o~t~tain:in{, Z n -

orderknt,,

their

no

[ i la.Lium J,)ns ill }~-sites spinel

on

cation

~nd

the

]!'e,, ~_0!

the

or N b 5 +

of

preference

and

,~{mtetimes

th( ~ s l e r i e :~+ ol Zt~. ions

distribui

of

Sb 5+

the

foF

Lio.

the

one

positions

d[fi e r s

of

la|ter

lar~er

spin( I

cation

the

ral

1he

is t,e p o r l ¢,(I ] ll'I/ .

in

to

t~<~ti,,st ~,

{)J I }le,~( i o n s

t~ A - s i t e s


re~'ard

acts

t)rderiz,t,,

1.2
With

becomes

e(,ncentr~tion

/00/ .

however~

io

case

ions

influence

in

lithium

lai ter

expressed

the

due

between

the of

ease

as

cations,

Ti %+)

nels°

deform~lJon

ions

(Fet++

An

whieh

elusl era

{.~. i n LiO.9~C°'~'.9~//Li~u.)~TJ 1o5/0~i

formation

and

or

structure

critical

furtl+er present i n tti,e s p i n e l s {,f t h e ¢,,en(,r~t/ ' ,2+ 2+ 2+ ') !I ~++ !I+ !I+ (Me2+:Zn , Cu , NJ , M#~+:; M e + : M n ~(~(' ~ "Fi )

that

former

the

is

- LiMn20 ~ solid

the

ions

macroscopic

LJ 0+ ~_ l,~e~+ .+ .)x I-0.5x /LI 0.5~ x

in

spinel

outlastin~%

.+ L I O . +5 x F e ~+ l - O . S x / ~"I O"+ .5

While

solut:ions

the of

the

approximately

solid

: 1.75 ~alue

distribution

sites

us

effect

spinel

of x farce

and

one~

simultaneous

reflected

the

Lio.sZno.5/Lio.sMnl.5/O]l

in

tetrahedra]

arises.

value

RelatiYely

pre~renis

formula

between

in

the

between

and

mostly

ions

distances bul

also

to

octahedm'al LJ-Nb-Li-Nb

~,]I]+ o c c u p a t i o n

Crystal chemistry of magnetic oxides

Lx-Li-Nb-Nb.

The

Likewise

extent

tion

the

structure

of ordering,

of the r e s p e c t i v e

tures

spinels

c a n be c o r r e l a t e d

octahedral se w h e n

sites

tendency

note

to the data

according

mobility

could

is v e r y

An anomalously

high

more

radii

and

in tin s p i n e l s

given

at

ordering

transition

caused

by the h i g h

stability

bution

of cations

necessitates

higher

transition

temperature.

of ions

effects

temperature

1.;

spinel

to

Due

and p o s s i b l y

seems

that

• Zn/Ti t2

• ~/Ti

Fig.

0.~

23. R e l a t i o n s h i p hedral

between

cationic

tetragonal

0.98 c o~

radii

distortion

Me2+/Me2+Me4+/O~

G97

the r a t i o

of the

r ( M e 2 + ) / r ( M e 4+) o/a~

spinels

for

/137/.

the

oetaand

the

ordered

to be

a redistri-

results

• Ni/Ge

tOO

Let us

the c a t i o n

*Mn,/~ "CoNi/6e

rMe4'

h a n d no

the o r d e r - d i s o r d e r

673 K w h e r e

•Zn/O~Cq/'6e

rMe_~~¢

tendency

e. g.

of the N i - G e

energy

the

011 the other

in increa-

appears.

of N i 2+ in the B - s i t e s . a larger

present

= 1 respectively.

below

cannot

distortempera-

quantities

consequently

where

/116/.

tetragonal

Both

in the T a b l e X I I I

temperatures

/i15/,

transition

important.

and r V I ( N i 2 + ) / r V I ( s n 4+)

be e x p e c t e d low and

of the

/117/.

increases

becomes

was f o u n d

P4132

order-disorder

of the ionic

of the ionic r a d i i

= 1.08

that

their

23 and T a b l e X I I I )

the p V c o n t r i b u t i o n

to an o r d e r i n g

group

i. e. m a g n i t u d e s

and

r V I ( 0 o 2 + ) / r V I ( s n ~+)

transitions

to the space

with ratio

(see Fig.

the r a t i o

to m i n i m i z e

belongs

309

in a

310

E. Pollert

Table

XIII.

Correla |ion

be tween

t. u r e s

(d" i n v e r s e

r;l i io

of

Ihe

t r ~ n s i t \ell I (~lllperaspknels

oe l,~hedr~

i

~,nd

e~, I [ ohio

1he

rltd i i

i on

h'ansil

Spinel

the

Ii-I¥

r

temper;tture

VI

(Me

2 + )./ r V l ( M ~ !~ )

.

l~,1

l/~ i

M~2TiO h

7?0

Zn2Ti04

k. i9

770-820

Mn2Ti0l~

t . " - ~.

] . ::;-)

tO40

1.37

4 .

Zn 0.8Co 1.2oe0 h

I]30-i170

l.hO

, ]]

Zn].25Ni0.75GeOzl

1210-123(I

i.'lO

~ I L~,

i.

P.

Delamoye,

A.

Michel,

C.

2.

Y.

Bill\el

, P.

Pc\x,

Bull.

3.

Y.

Billie|

, P.

Poix~

A.

Hardy~

:\. L e e e r ] ~ M.

R.

Acid.

Soc.

Nei.

Cbim.

Michel~

C.

~,

[ig6g)

8'I7

l!r. !I~7 [ ] 9 o I)

I{. A e a d .

soL.

~

/|21} ~

l 1,)6<{ ) 'I. A.

5.

5.1.

Nonstoiohiometrie

This the

subject scope

several /120/. i.

DESTABILIZATION

e.

remarks The

of

can

in

metal

ions

The

discussed

to

e.t:ions

ori~,,'ina

former

large

structure

the

te

is

up

le n o w

ide~l

stoiehiomeiry

g~nions

['ronl

lattice

cain

S ' I ' B U C T U H I , AND

R.

Ac~,d. S o \ .

C(IMPt:T]N{i

two

by

the

solid-g-~s

illustr;~ted

up

to

~tssumed

P~\>l:iS

l']'l)lll

the

~o

r~l t i o

l)e b e y o n d ~,

[i] . llN/ ~ i l l 0 /

b~, s l < ~ i e h i o m e t r i e ~

? ;iI~i S [

,{:l|

~ln(|

~illd Il]~tl tlt(

]';~Calleies

or

in-

,~Y

~ i i h

:[ ] . x e d

the

~ r ~ L n s i I i]r<~

spLne]

Mg'A120}t

~,~,-

respeelJvely.

ex~,mple

M~.A]90/! is

camposJtion

¢ 1' c;~ ~ :i o n s

~ralencies

equilibrJ~l

|be

{<.

t~>

,~asol%~es

structure.

~)]" t h e

by

the

s< , , m s

Jell:\Ileal.

c~Ln, h o w e % ~ r

spinel

and

rus|riel

f:iven e.

(,~I) ~ i s

t s ~ improper

~rariations

of Al.~()3 i n

preset%red

~re

differenl

in

efJ'eo

o1' p r o b l e m ~ sh[lZ[ o n l y

~ere

~,quation

beeolnes

presenl

and

be

the

ue

de[;~ils

by

~re

solubility

More

Given

controlled

ease

Consequenlly

eJ{amples.

the

cations

lencies

re

spinels

from

terstitial

Zt

~nd

~PINEL

;, ~rery l~r~ue Y i e l d

review.

condition

Deviations r~ttio

this

THE

(.

spinels

represents

of

the

OF

l{:tnet , |;. V i l [ c r s ~

,~±

thc~

reported

~,nd ~h~

M~'0.35\1, ,.,~ ~ o

si, ine]

L21/ .

whe-

Crystal chemistry of magnetic oxides

The

change

resulting

of the v a l e n c i e s properties

concentration

the

range

B-sites

/64/.

If

the

spinel

The

situation

of

takes

1% c a u s e s from

may

the

place

at

ideal

x" ~

,%

the

x"

within

by a b o u t

exceeds

a critical

phase

24.

The

part

x,,

the

type

spinels ~-Me203

of t e r n a r y

spinel~

T - tetragonal

Pollert,

with which

(Me3+=-- F e J + , A l J + , C r 3 + , compounds

of

the

(Me2+=

Zn 2+,

c a n be

considered

the

ordering

\~,~/ X I

,

Due

to

however,

that

large can

as

the

have

to be a s s u m e d

38,

I145

of p h a s e C - cubic

according

to

J. N o v A k ,

(1977)o

are

compounds

of

3+

/me5/3[]i/3/04

ordering

5:1

in B ~ s i t e s

can

occur

and

4+

/Me3/2. ~1/3/04_

Me4+=

case.

ions

K)

of V a c a n c i e s

as Me

2+-

2+ a n d

energy

spinels,

• 3+~.

the •

Me

limiting

of t e t r a v a l e n t

the C o u l o m b

Sol.

be w r i t t e n

formula

(1235

system.

M. N e v ~ i v a ,

concentration

M n 3+) w h e r e

general

cut

Mn-Cr-0

P. H o l b a ,

Chem.

Co2+,Mg2+,Cd2+,Mn

3:1

value,

x,, • o MnzOl

'

r

of i s o t h e r m a l

diagram

d. Phys.

defect

in

14 K

NOn ~ E.

The

tempe-

is s e p a r a t e d .

Cr Fig.

the

of M n 3+ ions

interval

x"

i/'

r/

the or

24.

x"

',c~,o,.c:,a ; ,

run"

concentration

and a second

x"

influence

sublattioes

tetragonal-to-oublc

of this

19 a n d

can

on the

"heating

of the

×"

\ ~ \ '

ions

stoiohiometry

i n Figs.

I

/

e. g.

unstable

l~,,.._....i.,.. ~ CrzO/ ~,,, "\,O

\~

ions;

the d e c r e a s e

become

metal

of c a t i o n s

a decrease

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

/

transition

Jahn-Teller

K and

deviation

structure

the

distribution

of h a u s m a n n i t e 1409-1460

by a b o u t

the

the

of a c t i v e

transformation rature

as

311

Ti4+,Ge4+,Mn

Their

existence

and Vacancies

contribution

as m e t a s t a b l e

is

in

lowered.

because

4+)

/120/.

is the

octahedral

The

heating

'the

conditioned

latter by sites.

structure,

at h i g h

enough

312

E. Pollert

temperatures

produces

stituents

or

to ~ v a c a n c y - f r e e

An

excess

of

cations

in

the

ideal

spinel

reasons

the

In

cases

some

appear

if

8;, s i t e s

C.. l i t h i u m

occupied

by

to

sites

inte

be

Due

to

minimize the

ions they

"~he i d e a

the

confirmed

by

influence

the

insertion

forces

are

from

an

~ 16c

site.

5.2.

Influence

Generally cations

the with

structural follows the is

of

extent re6ard

field

from

space

the

of

of to the

the

fiL~ure factor

by

the

V i

ry

cell

If

a

the

is

are



concentration which

electroslHtic

Li + ions

into

not

is

repulsion

the

of

found

to e / ~

with

=

(w{}

In

item

~a

h ~ s H r(,cksa]l 2+ ~+ Me / idd0!l ~,r

(Li+Me2+)16c/Me

reduced

lh,ees w i l h

pushed

product

the

is

sh;,re

M n 3+

with

in

the

MnlO!i

and

1.05!I.

en~'rt,T s e e m s

LiMnp0112 . Y h e

io b~'

Hrisin~,, L i + - L i +

stronc, enou{~,h I() d k s p l a e e

H I,i+

[oII

stability size

o~n

of

spinels

be

seen

of

the

stability

of

which

can

~ary

A2BO~I any 5n

containinc~

from

the

F[ G.

compounds

s~ructur~l

Hr(

tw<~ d i f f e r e n t L{5~ w h e r e K[ven. is

type

t h e r[~n(;'e of

0.5

-~ ~

the

As

].[mired

-~ 0 . 8

by ~nd

it

relation

volume

of

ions

V:i/V in

the

(, ::~8 ) elementary

cell

~nd

V

is

the

elementH-

n~olume.

pressure structural,

/12S/.

the

tons

one

(I) = where

M n 2+

c~l

incz'e}~ses.

that

existence the

enerc,T

resultin/~

empty

properties

their

fillin~

defined

the

and

I~e

structure

which

thai

of

are

ener~et teal

{e~leh l()e s i t ~

note

apparently

whLeh

con-

ma{,,Tlet i l e (~r h a u s m a n n i -

is h a l f

the

cation

repulsion

F e ]+

distortion

oxidic

occupalion.

sites

respectiYely

distribution

of

electrostatic 8c~ t o

int(, t h e 16c

sites.

us

the

the

to r o e k s a l t - l y p e

vacant

ions

J Is

into

silos

of

the

contribution

Let

16o

introduced

this

tetra~onal

the

spinel

electrostatic

LiMn~]O~

and

for

the

16c

8b

~ire f a v o u r e d

that

for

into

Because

M n 2+

with,~ a p e c u l i a r

sites

of

are

either

form.

li'i~. 8).

the

fill

F e ~]+ a n d

(Li+Me3+)16c/Me2+/16dOll.

consequently

(see

sites

neighborin{3

structure

octahedral

introduced

octahedral

There

order

type

can

tr}~nsition

nllotropic

structure

/12~/.

sites).

irreversible

}in e ~ / o l u t i o n f r o m

e.

te /122/, 8a

16c

the

is

applied

fields

filline, overlap

factor allotropic

can

be

ob~iously

transitions

chan¢;ed are

possible

and

because

,,12~/',

Crystal chemistry of magnetic oxides

[

313

~.i_.i..:7~;,:',, ," ," ,, ,"

i..: ,:J-t~,so,'_/>.'~,=// ,: ::,:"; :- ," : I.// I"

/

v

I

,

I

! ""

~ . . - ' l ~

t - T >,, ,~ : ~ :

"

~,/ ~

,, '

., / -A /

,,,

/.~ I,'"'~'1,7 ~-,<

\,(

V~----'~L'fj,I_"~L ~o

,

' , ~ ~_-:,,,'~.o,

,.-"

~ : ~"~d.\~.-~pt%~T.~'~ -

02

0,6

0.~

"

"

"

,~ . ~ , - ~ - ~ ' % ~

08

tO

12

l& r, [a]

Fig.

25. S t r u c t u r a l

fields

dependences

The p o s s i b i l i t y depends mutual

not

only

relation

of the i n t r o d u c t i o n on the a b s o l u t e between

(Me')A-O-(Me'')B. sites

spinel

structure

the

ionic radii examples

sidered

as

becomes

the l i m i t i n g

Table

XIV.

XIV|

the

tetrahedral oxygen

serve.

and

anion

As a n a p p r o x i m a t i v e may

ootahedral

is l i m i t e d

guide

and

the s u m of

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

Ag2MoO 4 and CdV204

of the ionic

radii

in some

c a n be

on con-

0.95

0.41

0.49

0.60

r (Me'')B/~ /

0.64

1.15

0.78

0.62

r(Me')+r(Me'')/~/

1.59

1.56

1.27

1°22

of the r e l e v a n t

coordination

to the c o v a l e n t

polyhedra

with high valency

effect.

bonds

Fe304

spinels

r (Me,)A/X/

similar

on the

the d i s t a n c e

the

cations

lattice

but also

MoAg204

(Me)A-O

have

radii

CdV204

of c a t i o n s

sites

the s p i n e l

enter

the spinels

Comparison

tire f o r c e s due

into

type.

cases.

Spinel

Reduction

parameter

to shift

unstable.

of the r e s p e c t i v e

in the Table

~-

of their

determining

cations

a possibility

of

of the A 2 M 0 4

of c a t i o n s

magnitudes

sizes

too large

simultaneously~

the

some

If

their

and course

at c o m p o u n d s

and

by

the

ZnFe204

electrostatic

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

of d I0 and d 9 c a t i o n s

atrao-

of the d i s t a n c e

i n the

tetrahedral

314

I~

E. Pollert

can

be

M3+iMe2+Fe3+ 2+ 2+

Cu

,Zn

iliustr';~ted

by

an

example

of

the

compounds

o:I:' the

~,,;ener~±

Yormul}~

)O!t w h e r e M3+= Y3+~EI,2~+~I~3+~YbJ+~Lu 3+ ~nd Me2+= M~;2+,Co ~~+ ,Mn ~+, .

/126-i~0/,

Fig.

.

.

.

',

26.

(,)

~O O oeo

-

g

o

~

0

Oc~00 O -

Fit';.

Occupation hinders ions

l'roln

cannot have

of the

enter to

be

the

26.

I'he e r y s t ~ l structure compounds /1']0/o

oet~hedral

possibility s terie tile ohanp:ed

sites

of

reasons

~nd

tetrahedral from

by

the because

sizes, the

larG'e

displaein~ Fe ~+

oubie

fhe to

oY b n [ l ' e

rare

::+

)

)( %

~nd

anions.

~i iendelloy

;t~'r~nG'emenl

llex~y')n~l

n

e~l'lh

oxygen of

I+k

with

of the

5'I trium

ions

Consequently Io the

Me 2+

co~q~]~ni oxypcn

sequence

b~)nd l~Lyers ,d

.l.;~yers

Crystal chemistry of magnetic oxides

... A B A B C A C A B C B C with

... w h e r e

five-fold

Me 2+ a n d

coordination

formed

Fe ~+ q ions

315

c a n be p l a c e d

by s h a r i n g

of

the f a c e s

into

the

sites

of t e t r a h e d r a

pairs.

The

dimensions

radii

rvl

appears. ionic

The

radii,

lattice.

Two

of the

> l~ a n d

octahedral

a tendency

limiting

cases

smaller

Their

principal

than

valency

:

At

relatively

small

in

the

12-fold

there

sites

If

of l a r g e

the r a t i o

is p r e s e r v e d

destroyed

The

and

compounds

network

by

CaFe204, the

unsufficient

siteso w i t h

Bi 9+ i o n w h i c h

of A g + ~

probably

cannot

they

oxygen

sublattice.

in s p i t e in

the

cations

substituted This

for

results

in

small

close

cations

packed

structural

corresponding

arrangement

types

to

of the

the

c a n be

oxygen the

anions

formation

formula

anions

is

are formed.

where

the

FeO 6 octahedra

edges

and

corners

is a n

form

a three

example

(see

dimensional Fig.

)

27.

of t h e i r spinel

spinel

oxygen

/132/.

Fig.

with

role.

of l a r g e

c a n be

cations

coordination

exist

a certain

the p l a c e m e n t

for

higher

phase.

and

the

different

sharing

plays

for

of the

ferrite-type

become

Ca 2+ a n d

concentrations

of h e x a g o n a l

MMe204

are

the r a d i u s

eventualities

distinguished

holes

to o c c u p y

Ootahedral

framework

of the

ideal

of C a F e 2 0 4

projected

along~003~

structure /131/.

27)

/131/,

316

If

E. P o l l e r t

the

cations

small or

the

olivine

share

eommon

dimensions

and

the

small

If

the

high

reaction

are

pressure

is

the

structure

Simultaneous stability values

of

the

in

standard

tetraheth-a Me()i~ and the m u t u a l

lattice

follo~s

while

from

are

too

phenacit

oetahedr~i M e O 6

relation the

MoLi20/l h~ts p h e n a c i t

J L transforms

~ 400o C

type

of

field of

to

Gibbs

4

the

the

between

[he

eomparison

of

structure

because

spinel

aeeordint~

to

the

Me2SiOll

(olivine)

-

Fig.

/134/'.

size is

enerf;ies

-

(spinel)

s~ructure

cation

-

28

Mo/Li2/0,,

both

structure

(olivine)

types

and

apparent

electron

eonl~iguration

the

comparison

the

phase

correspondin~

-

Me2GeO

-

to

4

Me2SiO~

-

overlap.

from

(spinel) (spinel)

I

F

Mg ~

i

6o! ~G o

eC0

2¢ 5o

30 20 get manor es

Fig.

with

cations.

applied

spinel

Me2GeO

plotted

holes

compounds

:

(phenaeit)

influence of

ootahedral

and

:

Li2Mo02| since

tbe

metals

spinels

of b o t h

/i~3/

in which

in

and

destabilized

in/'luenoe of

present

size

tetrahedral

also

The

of a l k a l i n e

MoNa204

of

the

is

formed,

are

edges.

of c a t i o n s

the m o l y b d a t e s

into

strueture

structure

their

MOAN204

introduced

spinel

28.

Standard olivine /134/.

free -

10

enthalpies

spinel

in

0 [k J/m0/J ~ G~

of

~4ermanates

transform~l~ion and

sil~ea~es

on ~JJ the

transitions

the

Crystal chemistry of magnetic oxides

Higher

stability

germanate

of

spinels

all by the e l e c t r o n c o n f i g u r a t i o n more

suitable

of the s t a b i l i t y f r o m N i - s p i n e l this r e a s o n

the most

is formed.

stable

sites Zn2Ge04 Let us note

ions.

ones is c a u s e d above Further

their size is

o b v i o u s l y f r o m the

Spinels

c o n t a i n i n g Ni 2+ ions

ones w h i l e m a g n e s i u m

of M g 2+ ions for o c t a h e d r a l

Similarly with regard

tetrahedral

(3d10).

to M g - s p i n e l r e s u l t s

of the d i v a l e n t

of the small p r e f e r e n c e stability.

than the s i l i c a t e

of Ge 4+ ions

in c o m p a r i s o n w i t h Si 4+ ions w h i c h are too small. A d e c r e a s e

electron configuration are for

317

spinels,

sites~ have

to the s t r o n g p r e f e r e n c e

of Zn 2+ ions for

s p i n e l does not exist and the p h e n a c i t

that a p p a r e n t l y m a x i m u m

i n the o c t a h e d r a l sites exists

because

the lowest

concentration

structure

of Zn 2+ ions

in the s p i n e l phase Z n / Z n o . 3 N i 0 . 7 G e / 0 4

/135/,

11361. Similar

conclusions

f o l l o w f r o m the c o m p a r i s o n

of the s t r u c t u r a l p r o p e r t i e s

of the m i x e d oxides L i M e V O 4 (Me = Ni, Co, Mg, Zn). W h i l e L i N i V 0 4 and L i C o V 0 4 are spinels, struotures~

LiMgV04

the p r e s s u r e

configurations

of the spinel s t r u c t u r e of the cations p r e s e n t

Li/Crl.sSbl.5/04

the sequence

and p h e n a o i t e

into the s p i n e l one under

of 670 K /ll6/.

only by the i n f l u e n c e

of the electran

in the lattice can be o b s e r v e d in the

if Cr 3+ i o n s

The low t e m p e r a t u r e m o d i f i c a t i o n with

in olivine

and c a n be t r a n s f o r m e d

of 30 kb and at the t e m p e r a t u r e

Destabilization

antimonate

and L i Z n ¥ O 4 c r y s t a l l i z e

respectively

are p a r t i a l l y r e p l a c e d by Fe 3+ ions.

of the c o m p o u n d s

of the o x y g e n layers

has a h e x a g o n a l

... A B C A B A C A B C

structure

... and the d i s t r i b u -

tion of cations given by the formula (Lio.5)TI (Lio.5)T2 (Sbo.5)ol(OrFeo.5)O2 TI, 2 and 01,2 d e n o t e two d i f f e r e n t kinds of the t e t r a g o n a l and o c t a h e d r a l sites.

A n n e a l i n g at t e m p e r a t u r e s

random distribution

of c a t i o n s

above 1250°C

leads, however,

to the m o r e

and the s p i n e l

Lio.83Feo.17/Lio.17Feo.33Sbo.sCr/04 is

f o r m e d /137/.

ACKNOWLEDGEMENT

Author wish

to express his g r a t i t u d e

helpful difcussions

to dr S. K r u p i 6 k a

and c r i t i c a l r e a d i n g

and dr K. Z ~ v ~ t a for

of the m a n u s c r i p t .

REFERENCES

/I/

C. K i t t e l ,

/2/

E.J.W.

/3/

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Introduction

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2. edit.,

John Wiley

Inc. New Y o r k 1956.

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and E.L. Heilmann,

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J. Chem.

Phys. Rev.

J. Phys.

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J.B.

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S. I{rupiSka F.

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L.A.

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/20/

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Bacon,

/21/

S. Hafner,

/22/

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5ol.

AoI~

W.

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322

E. Pollert

Genera]

liter:~lure

S.

Krupi6ka~

d.

Smit ~ H.P.J.

D.J.

does

Physik

M~rsh~t]l~

der

Wijn~

D.J.

Craik

et

quoted

Ferrite

Ferlrites~

in Modern

Aoademie

not

Oxide

Press

und

in t h e

~erw~LndLer

m~{;nelisohe1"

Phi l i p s " l'eohnie;~l Libx'~t~) >hllerJ~lJs~

London-New

fil. i n Ma~{~netie O x i d e s , London-Ne~

~ext :

lid. 13. C ~ e k ~ y n e

York Ed.

York-Sydney-Toronto

Ox]{i( ,~ :\c~tdemi;,

[ ]'J-,q) :ir~,l

I).~.

,],~rle~,

[197:{)

D.O.

Cr~,ik~

[197% )

,b)h11 Wi](~y :~nd ~{~lls~

Crystal chemistry of magnetic oxides

323

THE AUTHOR

E. POLLERT

Emil

Pollert

Prague

where

graduated he

later

in 1961 received

work

in 1962

in the I n s t i t u t e

te),

Academy

of Sciences,

laboratory been

influenced

~ordeaux

His

of m a g n e t i c by his

in 1 9 7 3 - 7 4

main research

equilibria

his

interest

His

leisure-time

canoeing

also

of S o l i d

Prague

oxides stay

activity

the I n s t i t u t e

also h i s

PhD

The

and growing

of S o l i d

problems

connected

oxide m a t e r i a l s

of single

crystals.

to the p h o t o e l e e t r o e h e m i e a l activity

and d o w n h i l l

is d e v o t e d

skiing.

to sport,

like

Institu-

a leader

of the

of his w o r k

State

this

in

the r e s e a r c h

(now P h y s i c a l

he is there

with

Technology

with

orientation

cooperation

includes

started

Physics

1975

in the L a b o r a t o r y

of m a g n e t i c

of C h e m i c a l

. He

State

and since

technology.

and f o l l o w i n g

and c h a r a c t e r i z a t i o n phase

at

had

Chemistry

in

laboratory.

with

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

crystal

In the

properties

ohemistry~

last y e a r s of these

particularly

he

turned

materials.

white-water