Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 33–41 www.elsevier.com/locate/calphad Calculation of defect chemistry using the CALPHAD approach A. Nicholas Grundy ∗ , E. Povoden, T. Ivas, Ludwig J. Gauckler ETH Zurich, Department of Materials, Institute of Nonmetallic Materials, Swiss Federal Institute of Technology, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland Received 4 October 2005; received in revised form 18 November 2005; accepted 23 November 2005 Available online 19 December 2005 Abstract The defect chemistry of the perovskite phase LaMnO 3±d is modeled using the compound energy formalism and an associate model. In both cases the CALPHAD methodology is applied meaning that all thermodynamic and phase diagram data of the phase is simultaneously and consistently reproduced. The differences between the two modeling methods are discussed and the descriptions are submitted to a defect chemistry analysis. It is shown that the compound energy formalism is able to perfectly describe the defect chemistry of the perovskite phase whereas the associate model fails to correctly reproduce it. When using the associate model the choice of which associates to use plays a crucial role on how well the system can be approximated. As the associates are not physically meaningful entities this choice must be made arbitrarily. In the case of the compound energy formalism on the other hand a more physically realistic description of the system is achieved and fewer optimizing parameters are required. The reason for this is that the model description of the phase within the compound energy formalism is unambiguously constructed based on measured physical properties of the phase. The advantage of the associate model is that the model description is simple compared to the rather cumbersome expression obtained for the compound energy formalism. c  2005 Elsevier Ltd. All rights reserved. 1. Introduction The LaMnO 3±d perovskite is a very good candidate to compare different CALPHAD models to describe defect chemistry as it displays complex defect chemistry behaviour with both oxygen excess and oxygen deficiency, large defect concentrations and also a lot of experiments exist to validate the modeling results. It is largely due to the defects that doped LaMnO 3±d has so many interesting properties such as giant magnetoresistivity [1] and is currently the most widely used material for solid oxide fuel cell cathodes [2]. In turn, it is due to these manifold properties and applications that so many experiments have been conducted on this material. The experimental data on the undoped LaMnO 3 and (La, Sr)MnO 3 perovskite are assessed in detail in two previous papers [3,4]. The observed defect chemistry is due to the fact that the Mn ion on the B-site can have the valence states 2+,3+ and 4+ in the perovskite phase. Under reducing conditions an oxygen deficient perovskite, LaMnO 3-d , is obtained by the reduction of Mn 3+ to Mn 2+ . Oxygen is liberated and oxygen ∗ Corresponding author. Tel.: +41 1 632 6431; fax: +41 1 632 1132. E-mail address: grundy@mat.ethz.ch (A.N. Grundy). vacancies are formed thus maintaining charge neutrality. Under oxidizing conditions apparent oxygen excess, LaMnO 3+d , is observed. In this case Mn 3+ is oxidized to Mn 4+ and equal amounts of vacancies are formed on A- and B-sites again maintaining charge neutrality. Oxygen excess should therefore more correctly be referred to as cation deficiency. A further important defect reaction that occurs is the charge disproportionation, or charge dismutation reaction by which Mn 3+ partially disproportionates into Mn 2+ and Mn 4+ leading to good electronic conductivity even of stoichiometric LaMnO 3 [5]. This reaction can be considered to be entropy driven and occurs to significant extent due to the relatively unstable electron configuration of Mn 3+ [6]. In previous papers we have shown that the CALPHAD approach is well suited to model the defect chemistry of this phase. However, in the defect chemistry community there still remains some doubt as early attempts to model the LaMnO 3 perovskite phase using the CALPHAD approach with an associate model led to a wrong reproduction of the defect chemistry [7]. In this paper we compare the calculated defect chemistry when modeling the phase using an associate model and the compound energy formalism. A review on the details of these models is given by Saunders and Miodownik [8]. 0364-5916/$ - see front matter c  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2005.11.004