Abstract
An analysis of the effective radii of vacancies and the stoichiometric expansion coefficient is performed on metal oxides with fluorite and perovskite structures. Using the hard sphere model with Shannon ion radii we find that the effective radius of the oxide vacancy in fluorites increases with increasing ion radius of the host cation and that it is significantly smaller than the radius of the oxide ion in all cases, from 37 % smaller for HfO2 to 13 % smaller for ThO2. The perovskite structured LaGaO3 doped with Sr or Mg or both is analyzed in some detail. The results show that the effective radius of an oxide vacancy in doped LaGaO3 is only about 6 % smaller than the oxide ion. In spite of this the stoichiometric expansion coefficient (a kind of chemical expansion coefficient) of the similar perovskite, LaCrO3, is significantly smaller than the stoichiometric expansion coefficient of the fluorite structured CeO2. Our analysis results indicate that the smaller stoichiometric expansion coefficient of the perovskites is associated with the restraining action of the A-O sub-lattice to dimensional changes in the B-O sub-lattice and vice versa.
Highlights
IntroductionEven though the basic knowledge behind these phenomena was available several decades ago [5,6,7] there has been a lot of discussion and disagreement about the volume of the oxide vacancies including many years of debate about whether the volume of a vacancy is larger or smaller than that of the oxide ion
The performance of fluorite and perovskite structured metal oxide ceramics is very dependent on the volume changes that are associated with the necessary substitution of some of the host ions with lower valent metal ions to introduce ionicC
We have chosen to estimate the size of vacancies using the Shannon radii of the ions [13] and represent them as hard spheres in direct contact in the crystal unit cell because this is a simple method that is very easy to apply in ceramic engineering
Summary
Even though the basic knowledge behind these phenomena was available several decades ago [5,6,7] there has been a lot of discussion and disagreement about the volume of the oxide vacancies including many years of debate about whether the volume of a vacancy is larger or smaller than that of the oxide ion. We have chosen to estimate the size of vacancies using the Shannon radii of the ions [13] and represent them as hard spheres in direct contact in the crystal unit cell (hard sphere model) because this is a simple method that is very easy to apply in ceramic engineering. As a matter of fact the hard sphere model usually does not give the exact bond lengths and unit cell volumes measured using X-ray or neutron diffraction (XRD, NRD), but the approximation is sufficiently good for many purposes This model seems very useful even in case of crystals with relatively high concentrations of vacancies that introduce a significant additional uncertainty because the oxide vacancy will change the CN of the cations. It is worth noting that the properties that we are interested in are often those of the oxides at elevated temperatures (such as 500–1000 °C), whereas the Shannon radii are for room temperature
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