Relationship between surface area and crystal size of pure and doped cerium oxides

Pure and Zr, La or Pr-doped cerium oxides were characterised by transmission electron microscopy (TEM), N2 adsorption-desorption at −196 °C and X-ray diffraction (XRD). For crystal sizes calculation, the Scherrer and Williamson-Hall equations were compared, and the relationship between surface area and crystal size was critically discussed. It was demonstrated that the Williamson-Hall equation must be used instead of the Scherrer equation to calculate crystal sizes, since the latter equation underestimated the crystal size while the former one provided suitable values by taking into account the strain contribution to line broadening. The miscalculation of crystal size by using the Scherrer equation affected both pure and doped cerium oxides, but the size underestimation became more important for high dopant loading. Under the conditions of the BET surface area measurements, N2 molecules were adsorbed on the surface of the single crystals identified by XRD.