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Debye Scherrer Equation Full Width At

In other words since can be positive or negative, the absolute value must be taken and it reflects the half width of the shape line deviation in 2 axis (full width at half maximum height, ).

Shape factor of K can be 0.62 - 2.08 and is usually taken as about 0.89.

But, if all of the peaks of a pattern are going to give a similar value of L, then.cos must be identical.

This means that for a typical 5nm crystallite size and Cuk 1 0.15405 nm the peak at 2 170 must be more than ten times wide with respect to the peak at 2 10, which is never observed.

The purpose of modified Scherrer equation given in this paper is to provide a new approach to the kind of using Scherrer equation, so that a least squares technique can be applied to minimize the sources of errors.

Modified Scherrer equation plots ln against ln(1cos ) and obtains the intercept of a least squares line regression, ln K L, from which a single value of L is obtained through all of the available peaks.

This novel technique is used for a natural Hydroxyapatite (HA) of bovine bone fired at 600 C, 700 C, 900 C and 1100 C from which nano crystallite sizes of 22.8, 35.5, 37.3 and 38.1 nm were respectively obtained and 900 C was selected for biomaterials purposes.

These results show that modified Scherrer equation method is promising in nano materials applications and can distinguish between 37.3 and 38.1 nm by using the data from all of the available peaks.

Keywords: X-Ray Diffraction; Nano-Crystal; Scherrer Equation; Hydroxyapatite 1.

Introduction X-ray diffraction is a convenient method for determining the mean size of nano crysta llites in nano crystalline bulk materials.

This can be attributed to the fact that crystallite size is not synonymous with p article size, while X-Ray diffraction is sensitive to the crystallite size inside the particles.

From the well-known Scherrer formula the average crystallite size, L, is:.cos K L (1) where is the X-ray wavelength in nanometer (nm), is the peak width of the diffraction peak profile at half maximum height resulting from small crystallite size in radians and K is a constant related to crystallite shape, normally taken as 0.9.

The value of in 2 axis of diffraction profile must be in radians.

Debye Scherrer Equation Full Width Half

The can be in degrees or radians, since the cos corresponds to the same number; 2 coscos 45 42 (2) It can be taken as 0.89 or 0.9 for Full Width Half Maximum (FWHM) of spherical crystals with cubic unit cells.

For an excellent discussion of K, a good reference is the paper Scherrer after sixty years in 1978 2.

In conventional approximation, the integrated width of the pure profile ( ) is separated from that of the observed diffraction profile ( B ) assuming that both profiles are either Gaussian or Cauchy 3.

If Gaussian profile is accepted, then 22 Bb 2 in the case of Cauchy B b, where b is the instrument profile width.

Normally, these are supposed to be either Gaussian or both Cauchy, then 22 mn or, mn respectively.

In order to separate the size and strain contribution: 4.tg.cos L (5) In the case of crystallite size and lattice strain, two diffraction peaks must be used to calculate two unknown parameters L and.

The Scherrer equation predicts crystallite thickness if crystals are smaller than 1000 or 100 nm.

The simplest way to obtain Scherrer equation is to take the derivation of Braggs Law, 2sin d.

Holding the wavelength constant and allowing the diffraction angle to broaden from a sharp diffraction peak from an infinite single crystal with perfect 3-dimeintinal order.

For many small nano crystals, diffraction from a lot of tiny crystals deviate from.

The value of correspond to FWHM or, which is approximately half of 2.