JNL: JPD PIPS: 223407 TYPE: PAP TS: NEWGEN DATE: 12/7/2006 EDITOR: CK

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 39 (2006) 1–6 UNCORRECTED PROOF

Complex dielectric behaviour duringformation of BaTiO3 by combustionsynthesisK S Martirosyan1, D Nawarathna2, J R Claycomb3,J H Miller Jr4 and D Luss1

1 Department of Chemical Engineering University of Houston, Houston, TX 77204, USA2 Department of Mechanical Engineering, University of California, Santa Barbara, CA93106, USA3 Department of Mathematics and Physics, Houston Baptist University, Houston, TX 77074,USA4 Department of Physics and Texas Center for Superconductivity, University of Houston,Houston, TX 77204, USA

E-mail: kmartirossian@uh.edu

Received 28 April 2006, in final form 26 June 2006PublishedOnline at stacks.iop.org/JPhysD/39

AbstractComplex dielectric behaviour was observed during the combustion synthesisof polycrystalline barium titanate in the presence of a 0.1–100 kHz acelectrical field. The ac conductivity (σ ) and relative dielectric permittivity(ε) attained their maximum values during the initial stage of the combustionat ∼850 ◦C before the temperature reached its maximum (∼1340 ◦C) andbefore complete conversion of the reactants to the product BaTiO3. Theduration of the ac conductivity and relative dielectric permittivity at 0.1 kHzwere much shorter (∼90 ms) than at 100 kHz (∼3 s). The low frequencyresponse is probably dominated by massive charge carriers (O2−, Ti4+ Ba2+),while that at high frequency by light charge carriers (electrons, holes). Thetemporal ac conductivity, relative dielectric permittivity and temperaturesuggest that most charge carriers were generated when the reaction rate wasmaximal.

1. Introduction

Many advanced ceramic materials are produced by self-propagating high-temperature synthesis (SHS), also referredto as solid-state combustion synthesis [1-4]. The processis characterized by extremely high heat release (1012–1014 W m−3), high heating rate (up to 106 ◦C s−1), temperature(up to 2000 ◦C) and short reaction time (few seconds).Following ignition by an external thermal source, a rapid(typically 0.1–10 cm s−1) high temperature reaction frontwith temperature gradient (order of 103 ◦C s−1) propagatesthrough the heterogeneous reactant mixture converting themto products.

Several experimental and theoretical investigationsrevealed that solid-state combustion synthesis generates atransient electrical voltage and current of up to 2 V and 100 mAduring the initial stage of combustion (before the temperature

attained its maximum) and residual magnetic fields of upto 10 µT during the post combustion period [5–15]. Thegeneration of the electrical field during metal high temperatureoxidation can be explained as being due to different rates ofdiffusion of positive and negative charge carriers through thegrowing oxide shell [13–15].

Most previous studies of electromagnetic field formationduring combustion synthesis were of the amplitude andduration of the generated fields and the relation betweenelectrical and magnetic signals and the local temperature.Mechanisms governing the evolution of the charge formation,electrical conductivity and domain polarization during thecombustion synthesis have still not been established. Inparticular, very few studies have determined the electricalconductivity during the combustion synthesis [16–18].

The goal of this study is to determine the qualitativeelectronic and ionic transport behaviour during the combustion

0022-3727/06/010001+06$30.00 © 2006 IOP Publishing Ltd Printed in the UK 1

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Figure 1. Schematic of the experimental system.

synthesis of dielectric polycrystalline, ferroelectric bariumtitanate (BaTiO3). We followed the electrical conductivity,relative dielectric permittivity, local temporal temperatureand the phase transformations using dielectric spectroscopy,thermometric and XRD measurements. This informationprovides insight into the generation of electrical and magneticfields during the combustion synthesis and is essentialfor developing of models predicting their evolution andmagnitude.

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2. Experimental system and procedure

Barium titanate was produced by combustion synthesis in airvia the reaction

BaO2 + 0.84TiO2 + 0.16Ti → BaTiO3 + 0.34O↑2

+(−�Ho298 = −889 kJ mol−1). (1)

The reactants were 99+% pure (Sigma-Aldrich ChemicalCompany). The titanium oxide and barium peroxide weredried at 115 ◦C for 5 h and then mixed with titanium powder(∼10 µm) for 1 h in a ball-milling machine.

Ten grams of the reactant mixture was loaded into analumina boat. Two Pt-electrodes (∅ = 0.5 mm) and a S-type(Pt–Rh, ∅ = 0.5 mm) thermocouple were fixed on a non-conducting ceramic plate at a distance of about 2 mm fromeach other (figure 1 A-A). The electrodes and thermocouplewere inserted into the sample to a depth of 2 mm from thesurface, so that a planar combustion front passed by theelectrodes and thermocouple at the same time. A chemicalmatch (Ti + BaO2 + Al2O3) was placed at the sample end andwas ignited by an electrically heated coil, the width of whichwas equal to that of the alumina boat. The electric currentto the ignition coil was terminated immediately after ignitionto prevent electrical interference during the measurements.The ignition generated a planar propagating combustionfront moving through the sample at a constant velocity of

1.6 mm s−1. Thus, the two electrodes and thermocouple wereexposed to the same combustion temperature. The maximumcombustion temperature of ∼1340 ◦C was lower than themelting temperature of either of the final products (∼1600 ◦C),the Pt-electrodes or thermocouple.

The experimental set-up, used to measure the compleximpedance, is shown in the schematic figure 1. The impedancewas measured by a SR 780 analyser (Stanford Researchsystems, Sunnyvale, USA) at various frequencies over therange of 100 Hz–100 kHz with an alternating electrical fieldof ∼5 V cm−1. The ac conductivity (σ) and relative dielectricpermittivity (ε) were determined from the real and imaginaryparts of the impedance Z by the relations:

σ = Re(Z)ge

(Im(Z) + gc)2, ε = ge

εoω(Im(Z) + gc),

where εo = 8.853 · 10−12 F m−1 is the permittivity of thefree space, ω the angular frequency of the applied electricalfield; ge and gc electrode and sample geometrical factors oforder unity. The dielectric response and thermocouple signalswere simultaneously recorded by a seven channel Omega Dataacquisition board connected to a PC. The overall accuracyof the experimental determination of the complex impedanceand temperature was better than 2%. The experimental set-updescribed in [9] was used to measure the temporal temperatureand electrical voltage generated in a plane perpendicular tothe direction of the moving planar combustion front. Theimpedance during the voltage measurement was 0.25 M�.

The phase transformation and product conversion duringthe combustion were determined by the quenched front method[19]. In these experiments, a reactant mixture is placed in acylinder 62 mm high and 72 mm in diameter with a conical holemeasuring 20 mm at its base and 1 mm at its tip. The cylinderis made of two separable halves to enable examination of theproduct properties after the reaction in completed. Followingignition at the base of the cone, the increase in the ratio of

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Complex dielectric behaviour

Figure 2. Frequency dependence of the relative dielectricpermittivity and ac-conductivity of the reactant mixture of BaO2,TiO2 and Ti.

heat loss to that generated by the reaction extinguishes thereaction front before it reaches the tip of the cone. Thequenching rate was estimated to be between 103–104 K s−1.The average combustion front velocity was determined fromthe time that the temperature wave moved between twothermocouples inserted in the sample at a distance of about10 mm. The composition profile within the reaction zone wasdetermined by XRD (Siemens D5000; Cu Kα radiation source)measurements in the range of 20◦ � 2θ � 80◦ with 0.1◦ min−1

steps.

3. Experimental results

We initially tested the dielectric properties of the reactantmixture. Figure 2 shows the relative dielectric permittivityε(f ) and ac conductivity σ(f ) of the reactant mixtureas a function of frequency at room temperature. Theac conductivity of the reactant mixture was low, between10−12 and 10−7 S m−1. While the ac conductivity increasesmonotonically with increasing frequency, the relative dielectricpermittivity decreases. This characteristic dielectric behaviourof oxide ceramic materials is attributed to phase lag in thecharge carriers response to the ac field. Hopping electronsbetween ions at localized sites are responsible for polarizationbehind the applied field as its frequency increases.

As the reactant mixture heats up during the ignition, thedecomposition of barium peroxide releases oxygen by thereaction BaO2 → BaO + 0.5O2 at about 500 ◦C. The highexothermic reaction between titanium and oxygen becomesthe driving source of the combustion synthesis of BaTiO3.After initiation, the self-sustaining planar combustion frontpropagates through the solid reactant mixture converting it tobarium titanate. Figure 3 shows the local temporal temperature(Tc), and temperature gradient as the planar combustionfront passed by the thermocouple. Figure 4 describes thecorresponding in situ ac conductivity and relative dielectricpermittivity for two frequencies (0.1 and 100 kHz) as the planarcombustion front passed by the electrodes. Inspection showsthat at 100 Hz a sharp increase in ε and σ occurs when thecombustion temperature is about 850 ◦C. The duration of thedielectric response ε(f ) and σ(f ) at 0.1 kHz were about 90 ms.

Figure 3. Temporal local temperature and normalized temperaturegradient during the combustion synthesis of BaTiO3 by reaction (1).

Time, (S)

Figure 4. Impact of the frequency on the temporal relative dielectricpermittivity and ac-conductivity during the formation of bariumtitanate by reaction (1): (a) at 0.1 kHz and (b) 100 kHz. The dottedline is the time at which the maximum dT/dt was attained(T = 850 ◦C).

At 100 kHz, both ε(f ) and σ(f ) increase smoothly and bothattain their maximum at ∼850 ◦C. The maximum of ε(f )

and σ(f ) always occurred before the temperature reached itsmaximum of 1340 ◦C (figures 3 and 4). Figure 4 shows thatincreasing the applied field frequency from 0.1 to 100 kHzincreased the duration of the dielectric permittivity and acconductivity signals to 3 s.

The temporal relative reaction rate can be approximatedas the ratio of the instantaneous temperature rise dTc/dt toits maximum value (at the inflection point of the temporaltemperature). Figures 3 and 4 show that the largest amplitudesof σ(f ) and ε(f ) at f = 100 Hz and f = 100 kHz are attainedclose to the time at which the temperature profile reachedthe inflection point. At both frequencies, the ac conductivitydecreased at temperatures higher than that at the inflectionpoint.

Figure 5 shows that the ac conductivity and permittivitysignals lasted longer at 10 kHz than at 1 kHz. Upon increasingthe frequency the magnitude of dielectric permittivitydecreases, while the magnitude of ac conductivity increases.

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Figure 5. Temporal variation of the ac-conductivity and relativedielectric permittivity during the formation of barium titanate bycombustion synthesis at 1 and 10 kHz.

Figure 6. Log–log frequency dependence of the maximal value ofthe ac conductivity and relative dielectric permittivity duringcombustion synthesis of BaTiO3.

Figure 6 shows that with increasing frequency the maximumof σ(f ) increases while that of ε(f ) decreases.

Figure 7 shows that during the combustion synthesis ofbarium titanate, an electric voltage was generated when themoving combustion front temperature was ∼800◦C. It attainedits maximum value at a temperature of 850 ◦C, close to theinflection point of the temperature curve, at which the chemicalreaction rate attains its maximum. The voltage was annihilatedbefore the maximum combustion temperature of 1340 ◦C wasattained. This suggests that the electrical field formed whilethe titanium particles were partially oxidized.

It would be highly beneficial to know the charge con-centration or local product conversion to understand the rela-tion between the local temperature, electrical conductivity anddielectric permittivity. Unfortunately, the local charge carrierconcentration and product conversion could not be measuredin situ during the reaction. However, quenching of the com-bustion front in the copper cone allowed us to determine the

Figure 7. Temporal electric voltage and temperature generated by aplanar combustion front by reactionBaO2 + 0.84TiO2 + 0.16Ti → BaTiO3 + 0.34O2.

Figure 8. X-ray powder diffraction at three locations in the coppercone during the combustion synthesis of barium titanate in air.Patterns detected using the quench front method from locations at adistance x from top of the cone.

axial composition variation during the combustion synthesisof barium titanate. The combustion temperature in the middleof the sample (inside the copper cone) rose to its maximumvalue in 2.6 s. The average combustion front velocity was1.6 mm s−1. Thus, the average width of the combustion (pre-heating and reaction) zone was estimated as ∼4 mm. X-raydiffraction patterns of the quenched product at different dis-tances x from top of the copper cone (figure 8) show that partialoxidation of the titanium occurred at a distance x ∼ 2 mm fromthe tip of the cone where the temperature was between 850–900 ◦C. This location is close to that at which the maximum acconductivity, electrical signal and chemical reaction rate were

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Complex dielectric behaviour

achieved. The XRD pattern shows that BaO, TiO2 and a smallamount of barium peroxiode were the main species present inthe combustion front zone. This suggests that partial decom-position of BaO2 occurred at this location. The transformationof the reactants to BaTiO3 was almost complete at x = 4 mm,close to where the combustion temperature attained its max-imum value. The biggest diffraction peaks were observed at2θ = 31.607 and 45.305◦ corresponding to interplanar spacingof 2.828 Å (110) and 1.99 Å (200) of BaTiO3.

4. Discussion

The electrodes and thermocouple were much smaller (0.5 mm)than the width of the reaction front (4 mm) and were located in aplane normal to the direction of the propagating planar reactionfront. Thus, it can be assumed that during the dielectric andthermometric measurements they were exposed to the sametemporal temperature and product conversion. An importantadvantage of our measurements is that they enabled relating theac dielectric response to the local temperature and conversion.The experiments revealed certain behavioural features of theac dielectric and electrical signals which are as follows.

• The maximum ac conductivity, relative dielectricpermittivity and voltage are generated well before themaximum combustion temperature has been attained;

• the duration of the ac dielectric response at 0.1 kHz ismuch shorter (90 ms) than at 100 kHz (3 s);

• the termination of the ac conductivity and relativedielectric permittivity can occur either before or after themaximum temperature is attained;

• an increase in the applied frequency decreases theamplitude of the relative dielectric permittivity andincreases that of the ac conductivity.

The effective electrical conductivity of ceramic materials (σe)

is thermally activated and follows the Arrhenius temperaturedependence:

σe = σ0 exp(−Ea/kT ), (2)

where σo is a pre-exponential factor (characteristic of thematerial), Ea, k and T are the electrical conductivity apparentactivation energy, the Boltzmann’s constant and the absolutetemperature, respectively. Thus, the electrical conductivity ofceramic materials increases with temperature. On the otherhand, the electrical conductivity (σp) of collisional plasma,which may form in the gas phase during titanium particlescombustion, satisfies the relation

σp =∑

i

q2i ni

mi(jω + βi), (3)

where qi , mi and ni are the free charge, mass and theparticle density of the ith species, respectively; βi is thecollisional frequency, j = √−1 and ω = 2πf is the angularfrequency [20]. The plasma–neutral collision frequency isβi = ∑

i ni〈Si · Vi〉. Assuming a typical plasma–neutralthermal velocity of Vi ∼ 106 m s−1, neutral atom densityof ni ∼ 1019 m−3 and a cross section for charge exchangecollision of Si ∼ 10−20 m2, we estimate that the collisionfrequency in our experiments is βi ≈ 105 s−1. Thus, withincreasing angular frequency the effective plasma conductivity

should decrease. This is consistent with the observations infigures 3, 4 and 6 of the non-Arrhenius temperature dependenceand non-plasma-like behaviour of the ac conductivity. Inaddition, it is well established that the conductivity of ceramicmaterials takes the form of a power law over a wide range offrequencies, i.e.

σ(ω) = σ(0) + Aωn, (4)

where σ (0) is the dc part and A the amplitude of the acconductivity. Equation (4) is the universal dielectric response(UDR) first reported by Jonscher for a wide variety of materialswith an exponent n in the range (0.5, 1) [21–24]. This exponentis used to characterize the electrical conduction mechanism indifferent materials. It is indicative of the interaction betweenthe charge species participating in the polarization. Forexample, in the quantum mechanical tunnelling conductionmechanism n is almost equal to 0.8 [24]. The frequencyexponent n is determined by the relation

n = d log σac

d log(w/2π). (5)

During the combustion synthesis of BaTiO3 the exponentis equal to 1.3 ± 0.1 (figure 6), which is outside of theUDR power law range. This indicates that the signal wasgenerated by a different conduction mechanism. The electricalconductivity behaviour indicates that non-equilibrium chargeconcentrations form during the initial stage of the combustionsynthesis. The reaction rate and corresponding rate of heatrelease attain their largest value in the vicinity of the inflectionpoint of temporal temperature. The ratio of the temperaturerise rate to its maximum value is closely equal to the relativereaction rate. Inspection of figures 3 and 4 shows thatthe maximum ac-response signals for frequencies 0.1 and100 kHz forms in the region in which the reaction rate becomesappreciable. Thus, σ(f ) and ε(f ) reach their maximumvalue at a temperature lower than the maximum combustiontemperature because of the vigorous production of positive andnegative charge carriers (electrons, holes, ions, vacancies) inthe combustion region.

The formation of the electrical voltage at temperatureslower than the maximum reaction temperature (figure 7) alsoconfirms that the generation of charge carriers occurs inthe early stage of combustion. This behaviour verifies themodel prediction [14] that most charge carriers are generatedduring the initial period of combustion, when the reactionrate is appreciable. Moreover, the generation of a voltagepeak before the maximum combustion temperature is reached(figure 7) rules out the possibility that thermoelectric and hightemperature electron thermal emission were the major sourcesof voltage generation, as their magnitude did not monotonicallyincrease with temperature.

The quenched front experiments (figure 8) showed thatBaTiO3 did not form during the initial stage of the combustion.Hence, it did not cause the rapid ac conductivity andpermittivity increase. Heat conduction from the approachingtemperature front during solid combustion heats the solidparticle in the pre-front zone. As the particle temperatureincreases to about 500 ◦C, the thermal decomposition of BaO2

to BaO and oxygen begins [25]. The model of the electric

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K S Martirosyan et al

field generation by high-temperature metal oxidation predictsthat ambient gaseous oxygen is adsorbed on the metal particlessurface via the reversible reaction O2(g) � 2Oads [13,14]. Theadsorbed oxygen forms lattice atoms, as well as interstitial ionsand vacancies in the oxide lattice by the reaction V++ + 2e− +Oads � V++ + O2−. Simultaneously, electron–hole pairs aregenerated via thermal ionization nil � e− + h+. Thus, duringcombustion synthesis of BaTiO3 the electrical conductivityis related to the concentrations and drift mobilities of thegenerated charge carriers in the reaction zone. These chargecarriers can be either electronic in nature, i.e. both electronsand holes or defects of either the anionic or cationic sublattice[26–28]. The ac conductivity at the high frequency is expectedto have been generated mainly by light mass charge carriers, i.e.electrons and holes. This signal decayed after the maximumcombustion temperature was reached and at a slower rate thanthe one at the lower applied frequencies. The more massivecharge carriers such as O2−, Ti4+ and Ba2+ contributed to theshorter ac response at the low applied frequencies. Thesesignals were attenuated before the maximum combustiontemperature was attained. Thus, the sharper peak at 100 Hz(figure 3) may be attributed to heavy negative ions such asO2− that are primarily located in the narrow combustion zone.These heavy charge carriers undergo maximal displacement atlow frequencies but because of their inertia do not contributesignificantly to the high frequency response. The ac fieldinduced dipoles formed by the redistribution of O2− ions inthe reaction zone surrounding the heavy metal particles alsocontribute to the low frequency dielectric response. Chargingof the capacitive oxide layer surrounding the burning titaniumparticles may also increase the low frequency relative dielectricconstant. At high frequencies, the field may penetrate a largefraction of the sample volume thereby increasing the signalduration.

5. Conclusions

Combined dielectric, thermometric and XRD measurementsconfirmed that the maximum value of ac conductivity andrelative permittivity were attained during the initial stageof the combustion synthesis before the temperature reachedits maximum ∼1340 ◦C, i.e. before the synthesis of productBaTiO3 was incomplete. During the combustion synthesis ofbarium titanate the critical exponent n of the ac conductivityis outside the UDR power low range and equals 1.33 ± 0.1.

The high concentration of the charge carriers formedduring the initial stage of the combustion synthesis wasthe primary source of the rising electrical conductivity.The duration of the ac conductivity and relative dielectricpermittivity during the combustion synthesis of BaTiO3

depends on the applied frequencies. Both signals were about30 times shorter at 0.1 kHz than at 100 kHz. We conjecturethat heavy charge carriers (O2−, Ti4+ and Ba2+) formed inthe combustion zone dominate the low frequency response,and are the reason for the short duration of the signals. Themuch higher inertia of the heavy charge carriers causes theirdisplacement at the high frequencies to be much smaller thanthat of the lighter charge carriers. The light charge carriers(electrons, holes) dominate the high frequency response, and

this is the reason for the longer duration of the correspondingsignals.

In situ dielectric spectroscopy and thermometric measure-ments are an attractive method for the investigation of rapidhigh-temperature self-sustaining chemical reactions.

Acknowledgments

We wish to acknowledge the financial support by the NSF, theTexas Center for Superconductivity, the Materials ResearchScience and Engineering Center at the University of Houston,the Robert A Welch Foundation (E-1221) and the Institute forSpace Systems Operations.

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QUERIES

Page 2AQ1For figures 3 to 7, the supplied figures and the figures in doc are different. We have used figures from doc file.

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