Quantitative three-dimensional characterization of critical sizes of non-spherical TiO2 nanoparticles by using atomic force microscopy

Since both size and shape of nanoparticles are challenging to be quantitatively measured, traceable 3D measurements are nowadays an issue. 3D nanometrology plays a crucial role to reduce the uncertainty of measurements, improve traceable calibration of samples and implement new approaches, models, and methodologies in the study of the nanomaterials. AFM measurement of nanoparticles with unusual shape represent a non-trivial challenge due to the convolution with the finite size of the tip. In this work, geometric approaches for the determination of critical sizes of TiO2 anatase bipyramids and nanosheets are described. An uncertainty budget is estimated for each nanoparticle size with the aim of assessing the different sources of error to obtain a more reliable and consistent result. The combined standard uncertainties are respectively less than 5% and 10% of the dimensions of bipyramids and nanosheets. Due to the stability and monomodal distribution of their critical sizes, bipyramids and nanosheets are suitable to apply as candidate reference materials at the nanoscale. Moreover, quantitative measurements of shape and texture descriptors are discussed in order to understand the quality of the synthetized batch.