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Solid State Ionics 177 (2

Defect properties of Ti-doped Cr2O3

Alan Atkinson *, Mark R. Levy, Severine Roche, Robert A. Rudkin

Department of Materials, Imperial College, Exhibition Road, London, SW7 2AZ, UK

Received 27 September 2005; received in revised form 21 November 2005; accepted 23 November 2005

Abstract

The defects in Cr2�xTixO3 (x =0, 0.2 and 0.3) were studied by a combination of X-ray diffraction, density and electrical conductivity

measurements supported by atomistic simulation. The results are consistent with the Ti being dissolved as Ti4+ compensated by Cr vacancies

which associate to form complex defects of lower energy. Ti doping gives n-type semiconductivity due to a small concentration of Ti3+ in

equilibrium with the complexes.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Gas sensor; Chromium oxide; Defects; Conductivity

1. Introduction

Ti-doped chromium oxide (CTO or Cr2�xTixO3) is currently

being used as a material for sensors to detect trace quantities of

reducing gases in air (such as CO or ethanol vapour) by

changing their resistance at temperatures in the range 300–

500 -C [1]. The sensing mechanism involves the trapping of

electrons by chemisorption of oxygen from air on the surface

of a semiconducting oxide. If the bulk oxide is n-type this

reduces the bulk concentration of electrons in the conduction

band, whereas if the oxide is p-type it increases the concentra-

tion of holes in the valence band. In the presence of small

quantities of reducing gas in air, some of the chemisorbed

oxygen is removed and the trapped electrons are returned to the

bulk. Thus for an n-type oxide the conductance increases

(resistance decreases) in the presence of a reducing gas, whereas

for a p-type oxide the conductance decreases (resistance

increases). The sensor response of CTO is typical of a p-type

semiconducting oxide [2,3]. For this mechanism to generate a

useful sensitivity for sensing trace quantities of reducing gases

in air, the bulk concentration of carriers must be low so that the

trapping of electrons by chemisorption makes a significant

difference to the bulk carrier concentration. Therefore in order

to understand quantitatively how these sensors work it is first

0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.ssi.2005.11.015

* Corresponding author. Tel.: +44 207 5946780.

E-mail address: alan.atkinson@imperial.ac.uk (A. Atkinson).

necessary to have a good understanding of the ionic and

electronic defects in the bulk oxide.

The bulk defect properties of pure chromium oxide have not

been convincingly established because the concentrations of

intrinsic defects are very low and equilibrium between the gas

phase and the bulk is not established at temperatures below

¨1000 -C. At temperatures above ¨1300 -C ‘‘high purity’’

chromia appears to be an intrinsic narrow band semiconductor

with a band gap of approximately 3.3 eV [4]. In an ionic

picture band gap excitation can be viewed as conversion of

2Cr3+ into a Cr4+ (valence band hole) and a Cr2+ (conduction

band electron). Below this temperature chromia is extrinsic and

carrier concentrations are dominated by unavoidable electri-

cally active impurities [5]. Lower valency cations (Li+ and

Mg2+) increase conductivity and show a dependence on

oxygen activity consistent with expected p-type acceptor

doping [6,7]. Thus Ti4+ would also be expected to increase

conductivity and show an oxygen activity dependence charac-

teristic of n-type donor doping (i.e. increasing with decreasing

pO2). However, Holt and Kofstad [8] found that although

chromia doped with 2 mol% TiO2 (x =0.04) did show n-type

behaviour at 1000 -C at low pO2, there was an apparent n to p

transition at pO2¨10�5 atm and, in air, the conductivity was

slightly lower than in undoped chromia.

The Ti substitution levels in CTO sensor materials are

considerably larger than that studied by Holt and Kofstad. For

material synthesised at approximately 1000 -C it has been

established that there is a solid solution with the corundum

006) 1767 – 1770

ww

Table 1

Measured densities and crystal lattice parameters

Parameter Cr2O3

(pdf)aCr2O3 Cr1.8Ti0.2O3 Cr1.7Ti0.3O3

Lattice constant,

a (A)

4.95876T (14) 4.9608T (3) 4.9623T (3) 4.9615T (3)

Lattice constant,

c (A)

13.5942T (7) 13.6029T (9) 13.6045T (9) 13.6045T (9)

Unit cell volume

(A3)

289.48T (3) 289.91T (5) 290.12T (5) 290.02T (5)

Density (g cm�3) 5.23 5.2415T (16) 5.0997T (16) 4.9845T (16)a From powder diffraction file 38-1479.

A. Atkinson et al. / Solid State Ionics 177 (2006) 1767–17701768

structure for x <0.4 [2,3,9] and sensors typically have x=0.2. It

is therefore difficult to understand why the conductivity is so

low and the sensor behaviour p-type, in such heavily donor-

doped material. Furthermore, the Ti solubility is very large for

an aliovalent ion and it is feasible that this, and the electrical

inactivity, could be due to Ti being dissolved as Ti3+ rather than

Ti4+. Thus the objective of this study was to clarify the defect

and electrical behaviour of Ti dissolution in chromia using

density measurements, X-ray diffraction (XRD), electrical

conductivity and computer simulation of defect energies.

2. Experimental

Compounds of nominal compositions Cr2�xTixO3+d (x =0.2

and 0.3) were prepared by ultrasonic mixing powders of Cr2O3

(Alfa Aesar puratronic, 99.997%, 0.7 Am particle size) and

TiO2 (Sigma Aldrich, 99.99%) for 5 min in an ethanol/water

mixture. The product was then ball-milled using zirconia balls

for 24 h and then reacted in air for various combinations of

time (up to 200 h) and temperature (1000, 1200 and 1250 -C).The reacted product was again ball-milled and then analysed by

XRD (Philips XPERT MPD, Cu K radiation and a Si standard).

It was found that a single phase solid solution could only be

obtained using long reaction times (� approximately 70 h) at

1000 -C. The higher temperatures always produced significant

quantities of second phase tentatively identified as Cr2Ti2O7.

Unit cell parameters were calculated using the software Cellref.

Crystal density was measured on powders by the density

bottle method and water as the liquid. The water used was first

distilled to remove dissolved air and the temperature during a

single density determination was measured and also maintained

constant to T0.5 -C. The nominal volume of the density bottle

was 10 ml and each determination typically used 5 g of powder.

Each measurement was repeated several times to establish the

reproducibility, which was found to be T0.0016 g cm�3. In

order to obtain this accuracy with the undoped powder, the

crystal size had to be increased to reduce errors caused by

residual air trapped (or adsorbed) on the particle surfaces. This

was done by annealing the powder for 2 h at 1200 -C.Electrical conductivity was measured on bars of approximate

dimensions 3�4�20 mm formed by isostatically pressing the

powders and sintering for 5 h at 1000 -C in air. The specimens

had a volume fraction of pores (vp) of approximately 35%.

Resistance was measured using the 4-point DC method with Pt

wire loop electrodes and corrected for the effects of porosity by

multiplying the measured resistance by the factor (1�vp)2.

Reducing oxygen activities were established using Ar/H2/CO2

mixtures metered through mass flow controllers and 4 h was

allowed for the specimen to equilibrate after each change of

oxygen activity or temperature. Although this was sufficient for

the conductivity to appear to stabilise at its new value, this is no

guarantee that true equilibrium has been reached, especially at

the lower temperatures. The oxygen activity was measured

using a zirconia oxygen sensor.

Atomistic static lattice simulations were carried out using an

ionic model and Buckingham pair potentials with parameters

previously derived [10]. The electronic polarisability of oxygen

ions was accounted for via the shell model and the effect of

defects on the lattice was simulated by partitioning the lattice

and then using the Mott-Littleton approximation. The lattice

was permitted to relax to minimise the internal energy by

varying the ion positions and lattice parameters through a

Newton-Raphson procedure. Defect calculations were carried

out using the CASCADE code [11] and the effects of defect

concentrations were simulated using the mean field approxi-

mation as implemented by the GULP code [12].

3. Results and discussion

3.1. Crystal density

XRD showed that the CTO specimens were single phase

corundum structure with negligible second phases in evidence.

The density and XRD lattice parameter results are summarised

in Table 1.

The lattice parameters and density measurements for

undoped chromia are in reasonable agreement with the accepted

values in the powder diffraction file. The results on CTO show

that Ti doping has a negligible effect on the lattice parameters

and the cell volume remains constant to within T0.03%.

However, there is a significant reduction in the solid density

with increasing Ti substitution, which indicates a reduction in

mass of the average cell contents. If we take the initial state for

dissolution of Ti in chromia is as TiO2, then (since oxygen

interstitials are known to have a high formation energy) the two

most likely dissolution reactions can be written:

3TiO2Y3TiCryþ VCrVVVþ 6O�O ð1Þ

and

2TiO2Y2TiCr& þ 2eVþ 3O�O þ

1

2O2 ð2Þ

Eq. (1) represents compensation of Ti4+ by Cr vacancies and

using the atomic masses of Ti (47.88)and Cr (51.996) the

density variation with x is given by

qx=q0 ¼ 0:3158þ 0:6842� 0:02695xð Þ= 1þ x=6ð Þ ð3Þ

Eq. (2) represents compensation by electrons and can also

be regarded as dissolution as Ti3+ depending on the degree of

ionisation of the neutral defect

Ti�CrYTiCr& þ eV ð4Þ

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

0 0.1 0.2 0.3 0.4 0.5

x in Cr(2-x)TixO3

Den

sity

rel

ativ

e to

Cr 2

O3

Ti4+ model

ExperimentTi3+ atomistic

Ti4+ atomistic

Fig. 1. Measured density of Cr2�xTixO3 compared with the expected variation

for Ti3+ (electron compensation) and Ti4+ (Cr vacancy compensation) dissolution

models.

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Log 1

0 (σ

/S c

m-1

)

x = 0x = 0.3

A. Atkinson et al. / Solid State Ionics 177 (2006) 1767–1770 1769

in which case the density variation is

qx=q0 ¼ 1� 0:02695x: ð5ÞThe measured densities are compared with the models in

Fig. 1 and clearly show that Ti4+ dissolution compensated by

Cr vacancies is the correct one.

3.2. Atomistic simulation

Atomistic simulations were carried out to calculate the

lattice parameters, unit cell volumes and solution energies for

the reactions in Eqs. (1) and (2).

The results in Table 2 indicate that dissolution as Ti3+ should

lead to a slight increase in unit cell volume whereas dissolution

as Ti4+ would give negligible change, in agreement with the

XRD results. The densities predicted from the atomistic

simulations are shown in Fig. 1. (Note that the errors given in

Table 1 correspond to a fractional error in the relative density of

5�10�4, which is too small to be indicated by error bars in Fig.

1). The ones for dissolution as Ti4+ compensated by Cr

vacancies are in good agreement with the experimental results.

The atomistic predictions for Ti3+ show lower densities than

predicted on the simple model due to the increase in cell volume

predicted by the atomistic simulation. The question now

remains as to whether Cr vacancy compensation is expected

to be energetically favoured. Using the results of the atomistic

simulation, the standard energy change of the reaction.

2Cr�Cr þ 6Ti�Cr þ3

2O2Y6TiCr& þ 2VCrVVVþ Cr2O3 ð6Þ

was calculated and found to be 1.89 eV per Ti. This implies

that in oxygen at unit activity Ti3+ is the more stable. A major

Table 2

Unit cell volumes and densities from atomistic simulation

Ti solution Parameter Cr2O3 Cr1.8Ti0.2O3 Cr1.7Ti0.3O3

Ti3+, electron Unit cell volume (A3) 282 288 291

Ti3+, electron Density (g cm�3) 5.370 5.284 5.241

Ti4+, electron Unit cell volume (A3) 282 282.7 283.1

Ti4+, electron Density (g cm�3) 5.370 5.206 5.124

contribution to the energy of the right hand side of Eq. (6) is

the Coulomb energy of the triply-charged Cr vacancy. This

can be reduced if it forms a neutral cluster with the Ti4+ ions.

The standard energy change for the reaction

2Cr�Cr þ 6Ti�Cr þ3

2O2Y2 3Ti

Cr& þ VCrVVV

� �� þ Cr2O3 ð7Þ

was calculated to be �1.39 eV per Ti, which indicates that

Ti4+ compensated by Cr vacancies is energetically favoured

by the formation of neutral defect clusters similar to ones

proposed for Ti in alumina [13] and in agreement with

earlier simulations [3]. In this cluster all the Ti4+ ions are on

normal lattice sites. Clusters involving interstitial cations, as

proposed by Ayub et al. [14], were found to have higher

energies. This is consistent with the XRD results which

showed no change in the relative intensities of the diffraction

peaks with Ti doping of the type reported by [14] for Sn-

doped chromia.

3.3. Electrical conductivity

The electrical conductivity results are presented in Fig. 2.

The conductivity of undoped chromia is almost independent

of oxygen activity indicating either intrinsic semiconduction

or extrinsic semiconduction controlled by fixed valence

residual impurities (e.g. Mg2+). The conductivity of the

CTO is very similar to undoped chromia in air. This is

surprising in view of the high Ti doping concentration and

indicates that most of the Ti is electrically inactive. The

conductivity of CTO increases as the oxygen activity

decreases. This indicates n-type semiconduction as expected

from a donor dopant. These results are at variance with those

reported by Holt and Kofstad [8] for CTO with a much lower

doping concentration x =0.04. The power law dependence

observed in our results is close to pO2

�1/8. The XRD and

density measurements and the atomistic simulations indicate

that most of the Ti is present in the form of Ti4+ in

electrically neutral complexes with Cr vacancies. These could

trap valence band electrons to give Ti3+ in the complex. The

-4.0

-3.5

-3.0

-15 -10 -5 0Log10 (PO2)

Fig. 2. Electrical conductivity of undoped chromia and Cr1.7Ti0.3O3 at 1000 -Cas a function of oxygen activity. The triangle represents a slope of �1/8.

A. Atkinson et al. / Solid State Ionics 177 (2006) 1767–17701770

resulting valence band holes would give p-type semiconduc-

tion, which is not consistent with the experimental observa-

tions. We therefore conclude that although the equilibrium in

Eq. (7) is to the right, favouring complexes, there is a small

proportion of Ti dissociated from the complexes. The

equilibrium constant for Eq. (7) predicts that the Ti3+

concentration (if the degree of dissociation is small) will

have an oxygen activity exponent of �1/4. This is greater

than the observed value (�1/8) and the discrepancy might be

due to sluggish equilibration kinetics or inadequacy of the

dilute model at such high concentrations. The reason why

CTO gives a p-type gas sensor response remains unclear and

will be addressed in a future publication.

4. Conclusions

Doping of chromia by Ti was found to give a solid solution

with negligible change in unit cell volume. The variation in

measured density with Ti concentration is consistent with the

Ti being dissolved as Ti4+ compensated by Cr vacancies. These

observations are consistent with atomistic simulations of the

solid solution which also indicate that the Ti4+ ions and Cr

vacancies form complex defects of lower energy. Ti doping

gives n-type semiconductivity due to a small concentration of

Ti3+ in equilibrium with the complexes that donate electrons to

the conduction band by ionisation to Ti4+.

Acknowledgement

The authors are grateful to R.W. Grimes for useful

discussions.

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