Kinetic Analysis of PbTiO 3 Phase Formation Via Diffusion Couple Method
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KINETIC ANALYSIS OF PbTiO3 PHASE FORMATION VIA DIFFUSION COUPLE METHOD Yun-Mo Sung and Woo-Chul Kwack Department of Materials Science & Engineering, Daejin University Pochun-koon, Kyunggi-do 487-711 Korea (South)
ABSTRACT A detail kinetic analysis was performed on the PbTiO3 phase formation reaction occurring via PbO-TiO2 diffusion couple experiments. The diffusion model of Pb2+ and O2- ions was used to derive the kinetics equation of PbTiO3 phase formation reaction. From the parabolic kinetics between the thickness of PbTiO3 layer and time, the reaction rate constant for PbTiO3 formation was determined to be a function of the average diffusion coefficient of Pb2+ ions. By substituting the diffusion couple experimental results into the present kinetics equation, average diffusion coefficient values of Pb2+ ions in PbTiO3 layer were calculated according to temperature values. The activation energy value for the diffusion of Pb2+ ions was estimated for PbTiO3 formation using Arrhenius plot and the equation for the diffusion coefficient of Pb2+ ions was determined.
INTRODUCTION Many of dielectrics, ferroelectrics, pyroelectrics and piezoelectrics, which are important electronic materials, are based on the perovskite oxide form (AIIBIVO3) [1,2]. For most of perovskite compounds, much study has been focused on their electrical properties and applications. In contrast, only limited number of study was performed on the formation reaction of perovskite phase [3-9]. Also, these studies were focused on isothermal kinetics such as Johnson-Mehl-Avrami analysis and/or non-isothermal kinetics such as Kissinger- [10] and Ozawa-type [11] analyses. All of these studies are based on the experiments using powder mixtures or thin film forms containing perovskite composition. However, a study on the formation of perovskite phase via interfacial reaction between AO and BO2 has never been performed. This bulk-type phase formation kinetics [12, 13] must be different from the powderand thin film-type phase formation kinetics. For the present study, a diffusion couple model was employed for the formation of PbTiO3 as an exemplary perovskite phase and a kinetics equation was derived using flux equations. The reaction rate constant (k) for the formation of PbTiO3 phase was precisely determined by employing parabolic kinetics.
DERIVATION OF A KINETIC EQUATION FOR PbTiO3 FORMATION A possible mechanism of PbTiO3 formation is the diffusion of Pb2+ and O2- ions in PbO through the perovskite interlayer. This is true since the dissociation energy between Ti4+ and O2- ions is so high and the flux of Ti4+ ions is relatively negligible. While the reactions at the PbO–PbTiO3 and PbTiO3–TiO2 interfaces can be expressed using the linear kinetics, transport F7.5.1
through the perovskite interlayer follows parabolic kinetics. The fluxes of Pb2+ and O2- ions were taken into account as follows: C Pb 2 + DPb2 + dµ Pb 2 + dφ + zF RT dξ dξ
(1)
C O 2 − DO 2 − dµ O 2 − dφ + zF RT dξ dξ
(2)
J Pb 2+ = − J O 2−
= −
Here, ηi is the
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