Dear Alexander,

Briefly, it is not indicated to use a simple function such as Scherrer equation to determine crystallite size of nanoparticles smaller than 5 nm. Usually, the diffractogram profiles for 20 nm (as you mentioned above) are not that bad, since you use it properly, and you can correlate it with other techniques ... but in the case of particles smaller than 5 nm, I would suggest you to use the Scherrer equation along with other techniques to evaluate the size of your particles (eg DLS, NTA, TEM, Zeta Potential etc). If your particles have 2 nm, I would say that you have no options unless you use TEM.

PS. Remember that, Scherrer equation will describe the contribution of the crystallite scattering in respect to the Bragg's Law condition for a specific reflection (plane), which is not always the limit of the particle size. In the case of big particles (more than 50 nm), you can find more than one crystallite into the particle. This is why you should corroborate your XRD data with other techniques.

I've used NTA (Nanoparticle Tracking Analysis) for this and I can say that is a good technique to determine nanosize particles, better than the conventional DLS.

Best regards.

Dear Alexander,

Briefly, it is not indicated to use a simple function such as Scherrer equation to determine crystallite size of nanoparticles smaller than 5 nm. Usually, the diffractogram profiles for 20 nm (as you mentioned above) are not that bad, since you use it properly, and you can correlate it with other techniques ... but in the case of particles smaller than 5 nm, I would suggest you to use the Scherrer equation along with other techniques to evaluate the size of your particles (eg DLS, NTA, TEM, Zeta Potential etc). If your particles have 2 nm, I would say that you have no options unless you use TEM.

PS. Remember that, Scherrer equation will describe the contribution of the crystallite scattering in respect to the Bragg's Law condition for a specific reflection (plane), which is not always the limit of the particle size. In the case of big particles (more than 50 nm), you can find more than one crystallite into the particle. This is why you should corroborate your XRD data with other techniques.

I've used NTA (Nanoparticle Tracking Analysis) for this and I can say that is a good technique to determine nanosize particles, better than the conventional DLS.

Best regards.

HRD only determine the crystalline part of the nanoparticle. For the exact size, the crystal lattice should be ideal, which is rare. TEM determine the entire size of the nanoparticle. It can have an amorphous layer. DLS and tracing analysis determine the hydrodynamic radius with water and electrolytes on the surface.

Dear Dr Bonturim and Prof. Mirgorod,

Thank you for your very useful comments.

So, is it possible to verify Scherrer calculated data for very small crystals (~2nm) if I have XRD of close powders (5-7 nm), which were studied by TEM technique, or broadering is too high?

Hi Alexander

You can refer to the attached article " Boundary Line of Microcrystallites in Amorphous and Crystalline Structures of Metallic Glasses", in which X-Ray Diffraction (XRD), Electron Diffraction (ED), Transmission Electron Microscopy (TEM) were used to define micro-crystallites in amorphous, short range ordered, structures and crystalline, long range ordered, structures of the Fe77Cr2B16Si5 and Fe74Ni4Mo3B17Si2 glasses, regardless to the contradiction between the data of the XRD and ED, by applying the mathematical relationship which originally derived by Scherrer.