Structure of cation interstitial defects in nonstoichiometric rutile

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Structure of cation interstitial defects in

nonstoichiometric rutile

L.A. Bursill, M.G. Blanchin

To cite this version:

L.A. Bursill, M.G. Blanchin. Structure of cation interstitial defects in nonstoichiometric rutile. Journal

de Physique Lettres, Edp sciences, 1983, 44 (4), pp.165-170. �10.1051/jphyslet:01983004404016500�.

�jpa-00232175�

Structure of

cation interstitial defects

in

nonstoichiometric

rutile

L. A. Bursill

_(*)

and M. G. Blanchin

Département de _Physique des Matériaux _(**), Université Claude Bernard, Lyon

I, 43, Boulevard

du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

(Re~u le 16 aofit 1982, revise le 14 decembre, accepte le _{3 janvier 1983)}

Résumé. - On

présente

ici de nouveaux _{modèles de défauts interstitiels pour accommoder la} non-stoechiométrie du rutile peu réduit

TiO2-x.

Ces défauts consistent en des _arrangements linéaires, le

long

de directions _[100] ou _[010], de

_paires

de cations trivalents situés au centre d’octaèdres

_d’oxygène

ayant une face en commun. On décrit ensuite les mécanismes de diffusion permettant

l’aggrégation

de tels défauts _{pour donner naissance à des}

_paires

de _plans de « cisaillement

_{cristallographique}

», ainsi que cela a été récemment observé en

_{microscopie électronique}

à haute résolution dans des cristaux

TiO2-x

refroidis relativement lentement

_depuis

la _température de réduction de 1 050 °C. Des consi-dérations relatives à

_{l’énergie électrostatique expliquent pourquoi}

ces défauts ont une

_énergie

de

formation et de

_{migration beaucoup plus}

_{basse que les défauts} « _ponctuels » traditionnels.

Abstract. - New cation interstitial defect models _are derived for substoichiometric rutile

TiO2-x.

These consist of linear arrangements,

along

[100] or

_{[010], containing}

two face-shared octahedral

pairs

of trivalent cations. Diffusion mechanisms are described

_whereby

these may

_readily

_aggregate to form

_pairs

of

_{crystallographic}

shear

_planes,

as observed _recently

by high-resolution

electron

microscopy, when

_{TiO2-x specimens}

are cooled

relatively slowly

from 1 050 °C. Electrostatic argu-ments

_{explain why}

these defects have very much lower formation and

migration energies

than the

traditional «

_point

defect » interstitial model. Classification

Physics Abstracts

61. 70B - 61. 70P - 61. 70Y

1. Introduction. - Considerable

uncertainty

remains

_concerning

the nature of the structural defects

_responsible

for the

_phase

_{Ti02-x (see}

_e.g. Akse and Whitehurst

_[1],

for a recent literature

survey).

Most

_{interpretations}

of

_physical

_property

and resonance

_technique

measurements have been based upon models for

point

defect

_equilibria

_(see

e.g. Kofstad

[2]).

Bursill and

_{Hyde [3] questioned}

whether « _{classical »}

_point

_{defects occurred in reduced rutile}

since

_{TiO 1. 9 9 8 61}

well annealed at 1 000 °C and then

_slowly

_cooled,

contained lamellae

_of

crystal-lographic

shear

_{planes (CSP) coexisting}

with a maze of

intersecting

{132} ~

0 2 2 ~

CSP. The

latter was identified as the nonstoichiometric

_{phase TiO~-~.}

_However,

the

_{interpretation}

of electrical

_conductivity

measurements

_by

_Baumard,

Panis and

_{Anthony [4]}

and of

_quenching

experiments

followed

_by

electron diffraction contrast studies

_(Blanchin,

_{Faisant, Picard,}

Ezzo and Fontaine

_[5])

_suggested

that for

_{Ti0i 99~0-2.0000}

the

_{equilibrium phase existing}

at 1 050 °C (*) Permanent Address : School of _Physics,

_University

of Melbourne, Parkville, 3052, Victoria, Australia.

(**) Associe au C.N.R.S.

L-166 JOURNAL DE _{PHYSIQUE -} LETTRES

contains no CSP.

_{High-resolution}

electron

_microscope

_(HREM)

studies of a number

_{of Tio2}

preparations

(0

x 0.003

5),

reduced at 1 323 K and

_given

a

_variety

of thermomechanical

histories,

showed new

_phenomena

(Blanchin,

Bursill,

Hutchison and Gai

[6] ;

Bursill,

Blanchin

and Smith

_{[7] ;}

Smith,

Blanchin and Bursill

_[8]).

Thus CSP were not

_present,

even en _miniature,

in non-deformed

_{crystals quenched}

from 1 323

_K,

_{but did appear,}

_frequently

as _very

closely-spaced pairs,

in more

_slowly

cooled or reduced and deformed

specimens.

HREM revealed both

lateral and

_longitudinal

disorder within the structure of the

_CSP,

the details of which were

strong-ly dependent

upon

cooling

histories.

Many

of the HREM

images

showed «

_{spot »}

contrasts

which

_suggest

_{the presence} of small

₍

20 A

_diameter)

defects. Recent electrical

_conductivity

studies over a wider _range of

_temperatures

(T),

and for

_{relatively high partial}

_{pressures of oxygen}

(p02)

(Marucco,

Gautron and Lemasson

_[9],

Gautron,

Marucco and Lemasson

_[10])

_suggest

that there are three domains within the

TiO 2 - x phase,

where the

predominant

defects are assumed to be :

I interstitial

_Tit.,

_prevailing

for T > 900 °C and for

_relatively

low

_partial

_{pressures of oxygen;} II

_doubly

ionized _{oxygen vacancies}

_{V,5, prevailing}

at lower

_temperatures

and for

_increasing

p02,

and

III another oxygen vacancy

defect, initially interpreted

as a

_single

ionized oxygen

_V,6

(Marucco

et al.

_[9])

but later attributed to _{oxygen vacancies associated with}

_{charge compensation}

of alio-valent

Me3+

_impurities

_{(Gautron et}

al.

_[10])

_prevailing

for x

0.000 16,

independent of p02

or T.

In this letter we

_present

new models for cation interstitial

_defects

which were derived in an

attempt

to extend the structural

_principles

of CS

_(previously

identified to

_{apply throughout}

most of the

_{stoichiometry}

_range

_{Ti0l,sooo-Ti02,oo00) to}

account for the structure of interstitial defects in non-stoichiometric rutile. New structure models for anion _vacancy and

_impurity

defects will be

_presented

elsewhere

_(Bursill

and

_Blanchin,

in

_{preparation).}

2. Derivation of interstitial structure. - 2 .1 TRADITIONAL CATION INTERSTITIAL STRUCTURE.

-Figure

la

_{depicts’the}

_[010]

bounded

_projection

_{(2013 ~}

y

i)

of the rutile structure,

using

the familiar octahedral

_{representation.}

_{The 4}

y

1

bounded

projection

is

symmetrically

equivalent.

(In

earlier work it was convenient to take the

_{corresponding [010]}

section,

see Bursill

Fig.

1. - Bounded

projection

(along

[100],

for - 4

x

_t)

of the structure of rutile,

containing :

a)

no _{defect ; b)} traditional interstitial defect, i.e. additional Ti 3 + cations ; c) two

pairs

of

octahedrally-coor-dinated Ti3 + cations

_sharing

faces; d), e) and _f) show linear extensions of c) to

produce

more widely-separ-ated _pairs of face-shared octahedra.

and

_Hyde

_[3],

the use of

_[010]

in the

_present

work

_{proved surprisingly}

instructive.)

Rutile is

tetra-gonal

with cell

_parameters

a = 4.593 7

_A,

_{space group}

_P4/mnm

with Ti at

_{000 ;}

_{2 i i}

and 0 at

uuO;

l~uO; 2

u,

2

+

U, i 2 and 2

+

_{u, 2 u, 2}

with u = 0.305 3.

Octahedrally

coordinated interstitial

sites _may be found at

_{~00; i02; 0~0; 0~}

_(see

Hurlen

_[11]).

_Figure

lb

_depicts

the classical model for the interstitial in

rutile,

whereby

a

Ti3 +

cation is

_inserted

at

_(~00).

Note the formation of a

string

of three face-shared

_octahedrally

coordinated cation

_sites,

_{separated by}

2.3

A,

Analysis

of the electrostatic valencies

_{(esv ;}

see

_{Megaw [12],}

for a discussion of this

concept)

of the oxygen

ions

_{(labelled 01}

and

₀₂

in

_{Fig. Ib)}

associated with this model

_{gives -}

2.00 for

₀₁

and - 2.5 for

_02.

The latter

_implies

a

_large

electrostatic _energy for such a defect. Bursill and

_{Hyde [3]}

showed that the CSP observed

_by

electron

_microscopy

and diffraction

_{techniques throughout}

most of the

_{stoichiometry}

_range

_{TiOl,sooo-2.000o}

all

_contain,

as a common structural

_principle,

pairs

of face-shared octahedra linked

_{by edge-}

and

_{comer-sharing}

in such a _way that

_they

_may

be

_regarded

as coherent

_intergrowths

of elements of the corundum-like structure of _e.g.

_Ti203’

with the rutile matrix. Our HREM observation that

_pairs

of CSP occurred

_frequently

in

_specimens

relatively slowly-cooled

across the

_{Ti02-x phase boundary}

_suggest

that the interstitial defects may consist of two

_pairs

of face-shared octahedra and that these then

_aggregate

in order to

pro-duce CSP. Thus

_figure

2a shows the octahedral _arrangement in a

[010]

bounded

projection through

a

_pair

of

₍₁₂₁₎

CSP. Note that cations in face-shared octahedral sites must have

_(formally

at

least) charge

+ 3 if the correct

_{stoichiometry}

_{(Ti2+, Ti~~ 2)}

_C~,-1

is to be obtained for the CSP. 2.2 ALTERNATIVE CATION INTERSTITIAL DEFECT STRUCTURE.

_{- Figure}

Ic shows that two

_pairs

of face-shared octahedra

_may

be

_readily

obtained from

_{figure 1 b by shifting}

one of the cations

(arrowed) by

vector

_[~00].

Such a

_jump

is

_{formally equivalent}

to a cation Frenkel defect.

However,

this

_{geometrical relationship}

is

_only

_superficial.

In order to obtain a

_pair

of CSP

_{by aggregation}

of the defects shown in

_figure

_Ic,

we

_require

a

Ti3 +

cation in each of the face-shared sites. We therefore take as our basic interstitial defect

_figure

Ic with four

Ti3+

cations. Two of these occupy octahedral interstices and two substitute for

Ti4+

cations in normal cation sites. In addition

Fig. 2. - Bounded

projection

(along

[100],

for - 4 x 4)

of the rutile structure

_{containing :}

_a) a

_pair

of (121)

crystallographic

shear

_planes

_{(CSP); b)} a _pair

_{of (253)}

_{CSP; c)} a

_{pair of (132)}

CSP and d) a

_pair

of

L-168 JOURNAL DE PHYSIQUE - LETTRES

one cation

_site,

_{formerly occupied by}

Ti4+,

is now _empty.

_Altogether

we have

_replaced

three normal

Ti4+

cations

_by

four

Ti3+ cations,

giving

no net

_change

in

_{positive change}

in the

_lattice,

compared

to the extra + 3

_charges

in the classical model. 2.3 ENERGETIC CONSIDERATIONS. - This

new defect model must

_have,

at least in

_principle,

very much lower electrostatic

contributions,

at both short and

_long-range,

to both its formation and

_{migration energies. Analysis}

of the electrostatic valencies _{of the oxygen sites show} two

crystallographically

distinct sites

_{(labelled 0~}

and

_0;

in

_{Fig. Ic),}

with 12

_0~

_having

esv = 2013 1.833 and 6’

_{0~ having}

esv = - 2.333. The _average esv is thus -

_2.0,

and we

_expect

that ion relaxations and associated

_polarization

of the oxygen ions

(rutile

has a

_high

dielectric

_constant)

will allow the esv of all of the _oxygen ions to

_approach

close to - 2.0.

_Simplistic

electrostatic _energy

cal-culations,

so far

_neglecting

ion relaxations and

polarization

effects,

using

a difference-sum

tech-nique,

showed that the new model is lower in electrostatic energy

_{by -}

100

_eV,

_despite

the fact

that it contains four

Ti3 +

cations

_compared

to one for the classical model

_(Bursill

and

_Shen,

in

_{preparation).}

More extensive calculations are in progress but it is

already

_{very clear that the} new model is an

extremely

efficient _way, both

energetically

and

chemically

to

_incorporate

Ti3 +

cations into rutile.

3. Further consideration and discussion. - 3 .1 MOBILITY

AND AGGREGATION OF INTERSTITIAL DEFECTS. - A

pair

of

₍₁₂₁₎

CSP _may be

_readily

formed

_(Fig.

_2a)

_by

ordered

_aggregation

of the defects shown in

_figure

_Ic,

_provided

that the defects are

reasonably

mobile.

_Assuming

a

homo-geneous distribution

of

such defects leads to the conclusion that CSP can form in the bulk of

a reduced

_crystal

and

thus are not constrained to _grow from the surface. Since the

_displacement

vector across a

_pair

of CSP is R = 0

[Modulo

1]

this

may occur without

_{necessarily creating}

a

_partial

dislocation

_{loop (of}

course, if dislocations

already

exist,

as in deformed

_specimens,

the defects may accrete to it and

_produce

_{dissociation;}

we return to elaborate the various

possi-bilities in another

_{paper). Figures}

3a,

b,

c indicate _sequences of

_cooperative

atomic diffusive

jumps

required

for

_{mobility parallel}

to

_{[001], [100]}

and

_[0~]

_{respectively.}

Note that we assume

such defects are created at the

_crystal

_surfaces,

_following

loss of _oxygen to the _gas

_phase

on

reduction of rutile. These

_jumps

can

_always

be carried out in such a

way

that

triple-face-sharing

of octahedra is avoided. Note that

_essentially

Frenkel defects are involved but in addition we

assume an

_accompanying

electronic

_{conductivity according}

to

Ti 3 + --+> Ti4 +

+ e-. This last

Fig. 3. - Arrows indicate

suggested

diffusion mechanisms for movement of Ti3 + interstitial defects

_parallel

to _{a) [001] ; b)}

_[010]

and _c)

_{[2 0 2].}

Dotted arrows _indicate more _complex concerted atom movements _required for bulk diffusion of M 3 + (e.g. Cr3 + or

Fe3 + )

interstitial defects.

process has a low activation _energy

( ~

0.40

_eV,

see Marucco et al.

[9]).

Similar diffusive

_hops

allow CSP

_{splitting, subsequent}

to their

_formation,

to

_{produce arbitrary separations}

_(see

Bursill

et al.

_[13]).

3.2 LINEARLY EXTENDED INTERSTITIAL DEFECTS. - Our HREM

observations showed that the local orientation of the CSP

_pairs

observed in

_relatively

_{slowly-cooled}

_specimens

fall between

(121)

and

₍₁₄₃₎

with mean orientation

_(132).

_Figures

2b-d show the

_{corresponding}

bounded

projections through pairs

of

_{(253), (132)}

and

₍₁₄₃₎

CSP

_{respectively.}

This

_{figure immediately}

suggests a further

_development

of the cation interstitial

_model,

_depicted

in

_figures

Id,

e, f. Here successive

_[~00]

atomic

_jumps

lead to further

_separation

of the face-shared

pairs, producing

linear defects

_having

extent

_starting

at 9.2

A

and

_increasing

to 13.8

_A,18.4

A

or 27.2

A

respective-ly.

Orderly aggregation

of such defects leads

_naturally

to

_pairs

of

_higher

index CSP.

Further-more,

imperfect ordering

of any one type, or of a mixture of different _types leads

naturally

to

lateral and

_longitudinal

disorder within the CSP _structure, as observed

_by

HREM. It should be noted that the linear

_strings

of

_displaced

octahedra

_connecting

the face-shared

_pairs

in these linear defects occur as elements of the

₍₀₁₁₎

_{antiphase boundary,}

or microtwin _{lamellar structures,}

often observed in rutile

_(see

Blanchin et al.

_{[6] ;}

Bursill and

_Hyde

_[3]).

The esv of the

_{corresponding}

oxygens are - 2.0.

3.3 INTERSTITIAL DEFECTS IN DOPED SPECIMENS. - We note that CSP defects also occur in rutiles

_doped

with

Fe3 +

or

Cr3 +.

The same interstitial defects models could

_apply

here,

with

Ti3 +

substituted

_by

_{Me3 +,}

_although

as

_yet

HREM has not been carried out to determine whether the CSP

_precipitate

as

_pairs.

(In

such cases

_long-range

diffusion mechanisms

_(dotted

in

_Fig.

_3),

are

required.)

Thus the kinetic behaviour of

doped specimens

is

expected

to differ from that of the reduced

_binary

_system

_Ti02-x.

3 . 4 LOCALIZATION OF ELECTRONS. - It has been convenient

so far to assume that Ti3 + ions

are

_(formally)

attached to the face-shared octahedral sites. In fact electrical

_conductivity

mea-surements

_suggest

_{(Marucco et}

al.

_[9])

that at T > 800

~C,

the effective

_charge

of interstitial cations is

_{Ti4 +,}

_{implying complete}

ionization

of Ti3 +

ions

_{(Ti3 +}

-~

Ti4 +

_{+ e -,}

₁₃

= 0.40

eV)

with _consequent delocalization of the electrons. Even at _very low

_temperatures

it is not certain that the

Ti3 +

ions will be located in face-shared octahedral sites. This appears to be the case for

Ti203,

and we

_regard

the shortest of the above linear defects as an element of

_Ti203

structure.

However

_{crystallographic}

studies of the

_phase

transitions of

_{Ti407 [14,}

_15]

show that in that

phase

Ti3+ -Ti3+

_pairing

occurs between

_edge-shared

octahedral

_sites,

with

_only

one of each

face-shared octahedra

_containing

a

Ti3 +

_ion,

for _temperatures below 125 K. At room tempe-rature and above all Ti ions have effective

charge

3.5,

indicating virtually complete

delocalization of the electrons.

_Clearly

the

_spatial

_extent of delocalization of electrons associated with small defects in

_{Ti02-x (x}

0.003

_5),

and its

_temperature

_variation,

remains an

interesting problem,

requiring

further

_experimental

and theoretical

_study.

4. Conclusion. - It is

now _necessary to seek further HREM evidence for the _presence and interactions of cation interstitial defects described here.

_Computer

simulations of HREM

_images

(Bursill

and

Shen,

in

_preparation)

show that it should be

_possible

to

_{directly image,}

and

_positively

identify,

such small

defects,

and their

_aggregation,

under _very

_{specific imaging}

conditions. In situ studies of the

_{precipitation}

and dissolution of

CSP,

and

_{complementary}

HREM

studies,

have

already produced positive

results and are in the course of

publication [13].

In another _paper the structure of oxygen vacancy defects in nonstoichiometric rutile is examined

(Bursill

and

_Blanchin,

in

_{preparation).}

It was

_again

found

_possible

to

_modify

the classical model and derive a structure consistent with the common structural theme referred to above.

_Clearly

L-170 JOURNAL DE PHYSIQUE - LETTRES

the

_principles

of

_point

defect

_equilibria

used for the

_analysis

of a wide _range of

physical

pro-perty

measurements

_{(electrical conductivity,}

_{thermogravimetry,}

ionic

_{conductivities,}

internal

friction,

electron-spin-resonance,

etc...)

will need to be

_carefully

reassessed in the

_light

of such models.

Acknowledgments.

- L. A. Bursill is

grateful

to

_University

of

_Lyon

for _support of a visit to

Lyon

in 1982. The work was also

_{supported by}

the

_University

of Melbourne.

References

[1]

AKSE, J. R. and WHITEHURST, H. B., J.

_Phys.

Chem. Solids 39 ₍₁₉₇₈₎ 451.

[2] KOFSTAD, P., Non

_{stoichiometry, diffusion}

and electrical conductivity in _binary metal oxides

(Wiley-Interscience, New

_York)

_{1972, p. 22 and 137.}

[3]

BURSILL, L. A. and _HYDE, B. G., Prog. Solid State Chem. 7 ₍₁₉₇₂₎ 177.

[4] BAUMARD, J. _{F., PANIS,} D. and ANTHONY, A. _M., J. Solid State Chem. 20 ₍₁₉₇₇₎ 43.

[5] BLANCHIN, M. _{G., FAISANT, P., PICARD, C., EZZO,} M. and FONTAINE, G., Phys. Status Solidi _(a) 60 ₍₁₉₈₀₎ 357.

[6] BLANCHIN, M. G., BURSILL, L. A., HUTCHISON, J. L. and GAI, P. L., J.

_{Physique Colloq.}

42 ₍₁₉₈₁₎ C3-95.

[7] BURSILL, L. A., BLANCHIN, M. G. and SMITH, D. J., Proc. R. Soc. Lond. A384 (1982) 135. [8] SMITH, D. J., BLANCHIN, M. G. and BURSILL, L. A., Micron 13 ₍₁₉₈₂₎ 245.

[9] MARUCCO, J. F., GAUTRON, J. and _{LEMASSON, P.,} J. _Phys. Chem. Solids 42 ₍₁₉₈₁₎ 363.

[10] GAUTRON, J., MARUCCO, J. F. and LEMASSON, P., Mater. Res. Bull. 16 (1981) 515.

[11]

HURLEN, T., Acta Chem. Scand. 13 ₍₁₉₅₉₎ 365.

[12]

MEGAW, H. D.,

Crystal

structures : a _working

_approach

_(Saunders, New _York) 1973, p. 39.

[13]

BLANCHIN, M. G., BURSILL, L. A. and SMITH, D. J., Proc. Inter. Conf. defects in ionic

crystals,

Dublin

(to be

_published

in Radiation

_Effects),

1982.

[14] MAREZIO, M., MCWHAN, D. B., DERNIER, P. D. and REMEIKA, J. P., J. Solid State Chem. 6 (1973)

213.