I have SEM images from ZnO nanoparticles whitch I've measured. Then I used the Scherrer equation to calculate the crystallite size but I can't get the result I expected, but a very smaller one.
Scherrer equation is extremely rough estimate of minimal possible size of crystals. In most cases it is meaningless. It uses peak broadening for calculations, but peak broadening has many causes, not only crystal size.
If your nanoparticles are bigger than max. a few tens of nanometres, then the Scherrer equation does not really apply any more. Also if the peak in your XRD measurement is broadened by other effects (e.g.overlapping peaks from your substrate) your estimated particle size will be smaller. Finally, depending on your SEM settings, charging of your particles may lead to your particles looking 'swollen', i.e. overstimation of the size there.
Arithmetic mistakes are usually done. In addition to overlapping of peaks problem as Dr. Brauns says, I advice you to check degrees radian conversion. And another thing, in a hexagonal nanoparticle, c axis is half of d-spacing, and you may never see it in SEM since the stacking is ABABAB...This is a simple trick that you may know.
Scherrer formula and W-H plots both can be used for the measurements of crystallite size and lattice strain.
According to the literature, crystallite size is a measure of the size of coherently diffracting regions/domains of a material. Crystallite size is equal to grain size if the grain is perfectly single crystallite. However grains of sintered samples contains several dislocations and defects, which, which interrupt the periodicity of the crystalline nature so an individual grain may contain a number of crystallites defined as coherently diffracting regions. XRD technique provides the information of these crystallite (coherently diffracting region) size present in the grains. Whereas the microscopic examination using SEM provides the grain size/ particle size of the material. Since grain contains many crystallites (coherently diffracting region), the crystallite size and grain size are not same. Similar results on crystallite size and grain size are reported in many references and few of them are listed below.
1. Arun Chamola, Hemant Singh, U.C. Naithani, Study of Pb(Zr0.65Ti0.35)O3 PZT (65/35) doping on structural, dielectric and conductivity properties of BaTiO3 (BT) ceramics, Adv. Mat. Lett. 2011, 2(2), 148-152
2. A R James, J Subrahmanyam and K L Yadav, Structural and electrical properties of nanocrystalline PLZT ceramics synthesized via mechano-chemical processing, J. Phys. D: Appl. Phys. 39 (2006) 2259–2263
3. Puja Goel, K. L. Yadav, Substitution site effect on structural and dielectric properties of La–Bi modified PZT, J Mater Sci (2007) 42:3928–3935
J. Paul Praveen, Kranti Kumar, A.R. James, T. Karthik, Saket Asthana, Dibakar Das, Large piezoelectric strain observed in sol-gel derived BZT-BCT ceramics, Current Applied Physics 14 (2014) 396-402
Scherrer equation is extremely rough estimate of minimal possible size of crystals. In most cases it is meaningless. It uses peak broadening for calculations, but peak broadening has many causes, not only crystal size.
Sherrer Eq gives you the crystallite size but SEM gives you a magnified image of your particles. if your particles are nanosize and also single crystal it should be close to the results from XRD and Sherrer eq depending on calibration of the device and may varies with different samples. if you have to know the particle sizes accurately you can use SEM or TEM or in some cases SAXS and DLS. Don't just depend on XRD data.
and of course there's always the possibility of errors in every methods.
SEM gives grain boundary image. In one grain boundary perhaps contain many particles. XRD data collected in small step size (eg 0.0001o) is better than large step size (eg 0.02o). But collecting XRD data with small step size is time consuming and costly. Calculation particle size (not grain boundary) from TEM image sometime is comparable to XRD data by using Scherrer equation.
The crystalline size by Scherrer formula using xrd will be always less than the grain size using sem.
Dear Dr. Andrea Vicente
Have a nice time and good day
Really, there are great differences between what can be measured by using the XRD and SEM.
X-ray diffraction can determine the crystallite size with high accuracy degree by using several well-known methods (Sheerer, Warren averbach, Rietveld refinement ..), where the incident X-ray will be diffracted from the unit cells of the growing crystallites. The obtained diffraction lines and their broadening reflect the degree of crystallinity of materials and their crystallite size, respectively.
If someone get diffraction peaks of have high intensity, this means that its material has high crystallinity degree. But the broadening has inversely proportion to the crystallite size.
But in case of SEM, one can obtain a surface image for a definite area selected by the technician. This area gives the grain size. Taking into consideration that the grain size is composed of an agglomeration of many particle size which consists of many crystallite size.
Thank you
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