-0.12 -0.06 0 0.06 0.12 0.18 0.24 0.3 0.36
1.8 1.84 1.88 1.92 1.96 2
αlmn
2-δ
1/2[100]
1/2[110]
1/2[111]a 1/2[111]b [100]
-0.12 -0.06 0 0.06 0.12 0.18 0.24 0.3
1.8 1.84 1.88 1.92 1.96
αlmn
2-δ
1/2[100]
1/2[110]
1/2[111]a 1/2[111]b [100]
Figure 2.11: Warren-Cowley short range order parameters (αlmn) as a function of nonstoichiometry for various pair clusters in the O2−/Vac sublattice at (a) 1262 K and (b) 1791 K. Of note is a strong clustering tendency along 1/2[110].
larger scale Monte Carlo calculations, can explain how electronic structure manifests in the behavior of macroscopic properties such as reduction enthalpy and entropy, electrical conductivity and so on. Also, the cluster expansion formalism is best suited for the study and characterization of defect associates[55, 56], which are often used to explain deviations in the non-stoichiometry behavior (and the dependent properties thereof) from that of an ideal solution of point defects.
a miscibility gap. The inclusion of vibrations resulted in quantitative corrections to the composition and temperature range of the miscibility gap, yielding excellent agreement with experiments. The solid state entropy change resulting from vacancy formation was evaluated and the deviation from ideal solution behavior illustrated through composition dependence of entropy. To further quantify the defect interac- tions leading to deviations from ideality, Warren Cowley short range order parameters were computed. It was found that there is a strong preference for vacancies to cluster along 1/2[110] and 1/2[111] directions, while the nearest neighbor 1/2[100] sites exhib- ited ordering behavior. While temperature does disorder the structure, the vacancy clustering behavior was shown to persist at temperatures as high as 1780 K.
Chapter 3
An electrical conductivity relaxation study of oxygen transport in
samarium doped ceria
3.1 Introduction
The remarkable capacity of ceria to display significant oxygen nonstoichiometry (δ) at high temperatures or low oxygen activity without changing its crystal structure is essential to many of its applications in solid state electrochemistry. Beyond its widespread use as a solid-oxide fuel-cell electrolyte when doped with trivalent el- ements such as samarium or gadolinium, nonstoichiometric ceria (CeO2−δ) has re- cently emerged as a candidate reaction medium to facilitate two-step solar ther- mochemical splitting of water and/or carbon dioxide to generate hydrogen or other fuels[19, 57, 21, 22, 58]. The first of the two steps is a high temperature endothermic reaction involving bulk release of oxygen. The second step, typically performed at a lower temperature, is the oxidation of the reduced ceria by the reactant gases (H2O and/or CO2) that returns the oxide to a low value of oxygen nonstoichiometry.
Whereas thermodynamics governs the theoretically achievable fuel productivity from this pair of reactions, that is, the fuel produced per cycle, the rate at which fuel is produced, the other critical metric, is a function of kinetics. Two serial steps are involved: diffusion of neutral oxygen species within the bulk of the oxide, quantified in terms of the chemical diffusion coefficient DChem, and reaction at the surface of
the oxide, quantified in terms of the surface reaction rate constant kS. In principle, DChem and kS are embodied in the time evolution of oxygen release or fuel produc- tion in a thermochemical experiment. In practice, however, the large driving forces (i.e. large changes in T and pO2), the random porous microstructure of the ma- terials commonly employed, and the poorly controlled gas flow dynamics of typical thermochemical reactors preclude access to these terms and impede meaningful com- parisons of the kinetic responses of candidate materials. In contrast to fuel production studies, experiments aimed at directly and quantitatively revealing kinetic properties must use small perturbations from equilibrium to avoid complex, non-linear effects, must employ well-defined sample geometries, and must present well-controlled gas flow dynamics.
A variety of techniques have been employed in combination with experimental configurations that meet the above requirements for measuringDChem andkS. These include secondary ion mass spectrometry (SIMS) to analyze isotope depth profiles[59], gravimetry relaxation[60, 61], electrochemical impedance spectroscopy[62] and electri- cal conductivity relaxation[63, 64, 65]. The objective of the present work is to demon- strate the versatility of this last method, electrical conductivity relaxation (ECR), to study the effect of temperature and gas atmosphere onDChem and kS.
In a relaxation experiment, one analyzes transient behavior in the re-equilibration process following a step change in thepO2 of the surrounding gas. The relaxation pro- file, typically that of sample mass or electrical conductivity, is described by a solution to Fick’s second law that takes into account the appropriate boundary conditions. A fit to the data yields values for the desired material parameters. The conductivity relaxation method is particularly attractive because of the ease with which electrical conductivity can be measured and with which reactors with small volumes, as re- quired for rapid exchange of gases, can be constructed. The long history of the ECR method, having been practiced as early as 1934 by Dünwald and Wagner[66], renders the technique, in some sense, a ‘classic’ tool. Furthermore, in some quarters, the level of sophistication in its application has yielded highly compelling results[65]. In many other instances, however, the experimental and numerical requirements for the suc-
cess of the method are not fully appreciated. Indeed, it has been recently suggested that a simultaneous determination of DChem and kS is inherently unreliable[67].
In the present study we have performed ECR measurements on bulk samples of Sm0.15Ce0.85O1.925−δ(samaria doped ceria, SDC15) to extract bothDChem andkS with the dual objectives of demonstrating the conditions under which both parameters can be reliably determined and providing new insights into this technologically important oxide. SDC15 is an ideal material against which to validate the experimental and analytical methodologies because the bulk transport properties are well-known and, though to a lesser degree of certainty, the surface properties are also known[62]. In addition, despite significant interest in SDC, surprisingly, comprehensive studies of its surface reactivity remain to be reported. Reports to date have either encompassed a limited range of oxygen partial pressures[60] or have focused on phenomena such as the influence of bulk grain boundaries[68], thin-film thickness effects[69], or the role of metal/oxide interfaces[70], each under a narrow range of conditions.
This chapter is organized as follows. Section 3.2 will briefly review the relevant theory for relaxation experiments and oxygen transport, followed by a brief analysis of anticipated results based on literature measurements of DChem and kS in SDC15.
In Section 3.3, the experimental details will be presented, followed by our data anal- ysis procedure and its test results. We will then discuss our results with SDC15 in Section 3.4 before concluding with Section 3.5.