mean grain (particle) size (rus. размер зерна (частицы) средний) — a property of compact nanomaterials and nanopowders which determines the specificity of their properties and applications.


The average size of grains or particles in nanomaterials and nanopowders is usually determined by the method of electron microscopy and X-ray diffraction. Electron microscopy is the only method that provides for the direct measurement of particle or grain size. Other methods, X-ray diffraction, sedimentation, photon correlation spectroscopy, gas adsorption, gas filtration, etc., are indirect. All methods have limitations in their applicability and none of them can be considered universal. Thus, electron microscopy is a local method and gives information about the size of the particles or grains only within the field of observation. Therefore, the investigated area of a substance or material should be representative and characteristic of the entire substance. In practice, the measurable sizes range from one nanometre to tens of microns. 

Among indirect methods, the most informative is X-ray diffraction, which makes it possible to determine the volume average size of grain, regions of coherent scattering. For this method, the average size, which is calculated from the broadening of diffraction peaks, lies in the range of 3-150 nm. Application of the method is complicated by the fact that the broadening of the diffraction peaks can be caused not only by small particles (smaller than 150 nm) or grains, but also the distortion of the crystal lattice and non-homogeneity, i.e., the heterogeneity of the bulk composition. Therefore, when interpreting X-ray diffraction data, it is necessary to distinguish the contributions of size, strain and non-homogeneous broadening to the experimentally observed value, and only use size broadening to estimate the average grain size. The particle size determined by the diffraction method is usually about 15-20% less than the size defined by electron microscopy.

Sedimentation, photon correlation spectroscopy, ultracentrifugation, gas adsorption and gas filtration are only applicable to powders, and their results are highly dependent on the degree of agglomeration of nanoparticles. Photon correlation spectroscopy makes it possible to determine the particle size in a range from 3 nm to 3 microns. The sedimentation method can explore particles larger than 50 nm. The gas adsorption and gas filtration methods measure the average particle size by the specific surface of the powder. Gas adsorption and gas filtration can be applied for the measurement of specific surface for powders with an average particle size of over 15 nm and 100 nm, respectively.


  • Gusev Alexander I.


  1. Gusev A. I. Nanomaterials, Nanostructures, and Nanotechnologies (in Russian) // Fizmatlit, Moscow (2007) - 416 pp.
  2. Gusev A. I., Rempel A. A. Nanocrystalline Materials. — Cambridge: Cambridge International Science Publishing, 2004. — 351 p.

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