Quantifying oxygen vacancies in neodymium and samarium doped ceria from heat capacity measurements

It has been previously reported in the literature that the vacancy concentration in a solid can be estimated using the linear term derived from low temperature heat capacity measurements. This paper investigates how such a model performs in both random and partially clustered vacancy systems. The heat capacity measurements were used to investigate the effect of singly (Nd or Sm) doped and co-doped (Nd and Sm) ceria, where simultaneous doping affects vacancy clustering and ionic conductivity. Comparison of calculated vacancy concentrations with sample stoichiometries showed that a vacancy concentration based on the linear term in the low temperature heat capacity is quantitative for near randomly distributed vacancies at low dopant concentration, but the prediction is low by approximately an order of magnitude when vacancies become clustered at higher dopant levels. This confirms that the linear term in the low-temperature heat capacity for non-metallic materials is a viable approach to estimate the vacancy concentration for randomly distributed vacancies which, in turn, can be used to distinguish between the random versus clustered vacancies.