# A thermodynamic and defect study of nonstoichiometric calcium doped cerium dioxide

#### Abstract

The aim of this investigation is to study the defect reactions and the associated thermodynamic behavior of calcium doped cerium dioxide as a function of nonstoichiometry. These defect reactions, involve the formation of oxygen vacancies, electrons, and holes which determine the nonstoichiometry, x, of the material as a function of temperature and oxygen partial pressure, $P{\sb{O\sb2}}.$ This work has studied the experimentally measureable defect reactions that occur across a range of temperature and oxygen partial pressure. It was found that both an n-type and p-type defect reaction determine the total nonstoichiometry x, as a function of measured temperature and $P\sb{O\sb2}.$ The enthalpy of formation associated with each defect reactions has been determined using to techniques. Coulometric titration analysis, determined that $\Delta H\sb{p}\sp\circ = -1.78 \pm .22\rm eV$ and $\Delta H\sb{n}\sp\circ = 4.44\rm eV.$ Constant Composition analysis determining that $\Delta H\sb{p}\sp\circ \approx -1.86\rm eV$ and $\Delta H\sb{n}\sp\circ = 4.44\rm eV.$ Also, the transition between the limiting case defect behavior and the effect on the apparent enthalpy of formation of oxygen has been defined in terms of the law of mass action. The results of this work in terms of an equation for the positive deviation from stoichiometry as a function of temperature and $P\sb{O\sb2}$ are presented as; $x\sb{n} = 4152.82e\sp-\sp{{(4.44eV)}\over{2kT}} P\sb{O\sb2}\sp{-1/4}-1.11(10\sp{-6})e\sp-{{(-1.78)}\over{2kT}} P\sb{O\sb2}\sp{1/4}$ while the negative deviation is defined as; $x\sb{p} = 1.1(10\sp{-6})e\sp-{{(-1.78)}\over{2kT}}$P$\sb{O\sb2} \sp{1/4}-4152.82e\sp-{{(4.44eV)}\over{2kT}}P\sb{O\sb2}\sp{-1/ 4}.$

#### Recommended Citation

Koehler, Charles John, "A thermodynamic and defect study of nonstoichiometric calcium doped cerium dioxide" (1998). *Dissertations (1962 - 2010) Access via Proquest Digital Dissertations*. AAI9842434.

https://epublications.marquette.edu/dissertations/AAI9842434