Scherrer’s formula

SEM micrograph of glass-ceramic samples 3 are shown in Figure 3 (a), (b), (c) and (d). It can be verified that the grain size calculated by the Scherrer s formula are well in line with the practical sizes measured by SEM. 

Each analytical instrument has a separate property, for example UV-visible spectroscopy helps to identify the surface plasmon resonance of synthesized nanoparticles. X-ray diffractometry identifies the crystaUine nature of synthesized nanoparticles and also using Scherrer s formula (D = K%l(3 cos 0) from which researchers are able to calculate the crystal size of synthesized nanoparticles. Fourier transform infrared spectroscopy finds the functional group which reduces metal salts into nanoparticles. The scanning electron microscope and transmission electron microscope indicate the exact size and shape of nanoparticles. Zeta potential plays a major role in nanoparticle characterization, which results in the stability and withstand property of nanoparticles. 

The average crystal size (D) has been calculated using Scherrer s formula (Guinier, 1963) based on the full width at halh maximum (FWHM) of the prominent peaks due to (111) plane. 

The reflection broadening in the XRD pattern is attributed to the contributions of the crystaUite size, microstrain and the instrument itself The crystal size D is inversely proportional to the peak breadth, according to the Scherrer s formula... 

With due reference to the previous researchers much attention was given to clarify selection and utilization of appropriate units of the main variables [38-41], used in Scherrer s formula, presented in Eq. 5.7. 

Table 5.33 Comparison of values of CS obtained from Scherrer s formula and look up chart...

The crystallite size can be obtained from the wide-angle X-ray scattering (WAXS) pattern of a silk fiber. Radial integration along the equator and meridian on the WAXS gives the radial peak width on the (200), (120), and (002) reflections. According to Scherrer s formula [85], the crystal size is... 

Table 5.1 Comparison of crystallite sizes calculated from the variance (s. ) and Scherrer (So) formula, with the area-weighted and volume-weighted < Ml > average sizes corresponding to different cases of simulated size distribution functions P n).

---