THE DEFECT STRUCTURE OF DONOR DOPED BaTiO3

HAL Id: jpa-00225531

https://hal.archives-ouvertes.fr/jpa-00225531

Submitted on 1 Jan 1986

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE DEFECT STRUCTURE OF DONOR DOPED BaTiO3

J. Baumard, Pierre Abelard, J . Lecomte

To cite this version:

J. Baumard, Pierre Abelard, J . Lecomte. THE DEFECT STRUCTURE OF DONOR DOPED Ba- TiO3. Journal de Physique Colloques, 1986, 47 (C1), pp.C1-867-C1-870. �10.1051/jphyscol:19861133�.

�jpa-00225531�

THE DEFECT STRUCTURE OF DONOR DOPED B a T i 0

J.F. BAUMARD, P. ABELARD and J. LECOMTE*

LA C.N.R.S. 320, Ecole Nationale Supérieure de Céramique Industrielle, 47 à 73, Avenue Albert Thomas, F-87Ô65 Limoges Cedex, France

* Laboratoire de Physique Electronique et de Thermodynamique des Oxydes, Faculté des Sciences, F-37200 Tours, France

Résume - Dans les oxydes ternaires, comme le titanate de baryum "BaTiC^", la concentration des divers défauts ponctuels dépend, à température et pression constante, de deux variables thermodynamiques, la pression partielle d'oxygène et l'activité de l'un des constituants, par exemple Ti0

. On propose une re- présentation synthétique des diverses configurations possibles pour les dé- fauts majoritaires dans le cas du titanate de barium dopé. On aborde la des- cription des effets entraînés par une composition cationique constante.

Abstract - In t e r n a r y oxides such as barium t i t a n a t e "BaTiO," the concentra- t i o n o±~the various p o i n t defects depends, a t constant temperature and p r e s - s u r e , on two thermodynamic parameters, the oxygen p a r t i a l pressure and the a c t i v i t y of an oxide component, such as Ti02. A s y n t h e t i c mode of r e p r e s e n t a - t i o n of the defect s t r u c t u r e i s proposed for t h e doped material and consequen- ces of a fixed c a t i o n i c composition are described.

I - INTRODUCTION

It has been known for a long time that additives entering the crystallographic latti- ce of barium titanate, or of its close analog strontium titanate, induce a deep modification of the electronic transport properties /1-5/. As for usual binary oxides, a meaningful interpretation of physical properties rests on a clear know- ledge of the defect structure. While the composition of pure binaries is determined once two thermodynamic variables, e.g., oxygen partial pressure and temperature, have been fixed under a constant total pressure, complete description of ternaries requi- res, according to the Gibbs phase rule, the specification of an additional variable, for instance titania activity for BaTiO,.

The present authors have recently proposed a new technique to depict the defect structure of ternary oxides /4,5/. This approach proved to be useful to derive the usual Kroger and Vink diagrams under the specific conditions of a constant cationic composition /4/. The purpose of the present paper is to extend the same ideas to the treatment of the defect chemistry in doped compounds, taking donor doped barium ti- tanate as an example.

II - BACKGROUND OF THE THEORY

As pointed out previously ,/4,5/, provided that two terms prevail in the charge balan- ce relationship, any concentration j j | of a point defect j should vary as :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19861133

JOURNAL DE PHYSIQUE

1 ^j 1 = Aj exp (- AEj/kT) @;Ih $!: ⁽¹⁾

where Aj is a constant including entropy terms,

AEj is an activation energy related to the energy of formation of defects,

N2 and aTi02 denote the oxygen partial pressure and activity of titania respectively,

m and n are simple fractional numbers or integers.

According to Eq. (I), the state of the compound is most conveniently described in a 3-dimensional space, the coordinates of which are Ln @ , ^{Ln a ~} , ⁱ 1/T. Isothermal ^~ sections of this space, or Ln pO - Ln aTiQZ plots, w i d be invesiigated here. In this representation, boundaries getween domains where successive two term approxima- tions of the charge balance hold are nothing but straight lines, in the vicinity of

which three majority point defects coexist /4/

111 - THE ISOTHERMAZ, REPRESENTATION OF THE DEFECT STRUCTURE

Several studies reported in the literature suggest that the Schottky type disorder i s the most probable intrinsic lattice disorder, as they support existence of oxygen /2/, barium /3/ and titanium /6/ vacancies. On the other hand, interstitial defects are generally disregarded on the basis of crystal-chemical considerations /I-2/. It is also generally accepted that enhanced n-type semiconduction results from a substitu- tional incorporation of cations possessing a higher valency, as ~ a 3 + or Nb5+. Large trivalent ions as La3+ would enter Ba2+ sites, while small pentavalent cations would substitute titaniums. Then the general charge balance reads :

2' 4'

1h.l + 2 l~i.1

ID'^

^{let[ + 2} j ~ + ~ 4 ~ lvTil l (2)

where D denotes a donor impurity. For a sake of simplicity, the defects will be assumed fully ionized.

In order to determine the variation of each defect concentration versus p12 and aTiO2, four additional equations are needed, that are listed in table 1.

Electronic disorder $ e' + h'

Schottky disorder 2' 4' 2.

,@ VBa

VTi

3 Vo

Reaction that alters the oxygen to metal ratio O/ (Ti

Ba) : 0 1

: *v;.

2e1

2 o2 (g) (111) Reaction that alters the barium to titanium ratio Ba/Ti :

Ti02= ~ i & + 2 + VBa 2'

: V (IV)

Table 1 : The important pseudo-chemical equilibria that describe the formation of m e f e c t s . Equilibria 1-11 preserve the stoichiometry of the compound, in oppo-

sition to equilibria 111-IV.

According to Eq (2), charge compensation of the dopant may occur through three possible modes :

ID'[

^{ie'l (3)}

ID'/

² lvBa/ 2' (4)

I0'I

lvTil 4' (5)

These simplified neutrality equations correspond to three schemes for the dopant incorporation :

Nb205 -+ 2 mii

2e' + 4 0 : + 1 2 o2 (g) ( 6 ) x 2'

BaO + Nb205

2 NbTi + B$, + 600 + VB, ₍₇₎

2 Nb205 > - 4 Nbii + 10 0 ;

VTi 4' ₍₈₎

plot

. ^The thermAynamic path followed by the compound under the assumption D s C 7 O is indicated by a broken line.

Fig.2. The variation of the various defect

concentrations versus oxygen p a r t i a l pres-

sure POZ. The variation of the t i t a n i a

activity (lines 1,2,3,4) mrresponds

to the respective _ behavior of the t h m -

dynamic path depicted i n Fig.1.

JOURNAL DE PHYSIQUE

The boundary between the domains where Eqs. (3) and (4) hold respectively follows from :

Introduction of Eq. (9) into the relationship obtained by application of mass action law to pseudo chemical equilibria of table 1 leads to :

where D denotes the concentration of donors. One observes that actually the boundary is a straight line in the Ln PO2 - Ln yiO plot. All boundaries may be calculated

"

L

according to similar principles and the entire diagram of Fig. 1 is then derived.

It is noteworthy to mention that the stability of barium titanate is limited both at large and low titania activities, due to precipitation of new phases as Bag Ti 0 and Ba Ti0 /7/. Within a first order approximation, boundaries are again parallefO

axis /s/.

to the Ln

The effect of a constant cationic composition

The experimenter generally prefers the condition of constant cationic composition to a constant component activity. A fixed ratio in the relative occupancy of A and B sites within the structure imposes a constraint in the Gibbs phase rule, that will make the titania activity itself a function of at constant temperature.

The condition of a constant cationic composition is simply expressed by :

where C is a constant, positive or negative, depending on the initial ratio Ba/Ti, the concentration of dopant cations, and the nature of crystallographic sites throu&

which the latter are incorporated. Introduction of Eq. (111, together with the char- ge balance expression, into the equations issued from the application of mass action law yield the thermodynamic path followed by the compound when the oxygen partial pressure varies. A typical variation has been sketched on Fig. 1 under the conditions D >> C > 0. The knowledge of the thermodynamic path enables to derive usual Krijger and Vink diagrams referring to the specific conditions under investigation (Fig. 2).

It is then straightforward to deduce the chemical compositions of the samples under the assumption of a complete equilibrium between the solid phase and the gaseous at- mosphere (Fig. 2.). A detailed discussion of the various cases encountered experimen- tally will constitute the subject of a forthcoming paper.

REFERENCES

/1/ Chan, N.H. and Smyth, D.M., J. Am. Ceram. Soc. 67 (1984) 285.

/2/ Chan, N.H. Sharma, R.K. and Smyth, D.M., 5. Electrochem. Soc. 128 (1981) 1762.

/3/ Daniels, J: and Hardtl, K.H., Philips Res. Repts, 2 (1976) 489.

/4/ Abelard, P. and Baumard, J.F., J. Phys. Chem. Solids, 43 (1982) 617.

/5/ B2uiiard, J.F. and Abelard P., Solid State Ionics, 12 (1984) 47.

/6/ Jonker, G.H. and Havinga, E.E., k t . Res. Bull., 32 (1982) 345.

/7/ O'Bryan, H.M. Jr. and ?hornson, J Jr., J. Am. Ceram. Soc., 57 (1974) 522.