Please note that it is correctly called the Scherrer equation, not the debye scherrer equation.

Note also that it is not particle size that is being estimated but crystallite size or effective scattering domain size.

Note also that unless you take into account instrumental peak broadening your results will be meaningless. There are very many discussions on here around this topic please do a search and have a read.

Dear  Gibong Yoon .

θ must be in radians,

θ=7.21 / 2 = 3,605 (degrees), becouse 2θ=7.21

θ(rad) = 3,605*2π/360=0,0629

So  cos θ = 1   and    D=48 nm.

But  β was calculated by formula

β = β(XRD) - β(stand) ,

where β(XRD) and β(stand) are measured widths at half maximum, of the

diffraction lines from the sample and the standard, respectively.

You must know β(stand) of your difractometr.

thank you^^

Tetiana R Tatarchuk 

Please note that it is correctly called the Scherrer equation, not the debye scherrer equation.

Note also that it is not particle size that is being estimated but crystallite size or effective scattering domain size.

Note also that unless you take into account instrumental peak broadening your results will be meaningless. There are very many discussions on here around this topic please do a search and have a read.

Dr. Ian Slipper

Very specific and qualitative information. Thanks for updation.

Dear Dr. Yoon,

FWHM You are using for calculation has to be corrected from instrumental broadening.

Instrument itself have its own broadening, that can be measured using Si standard. It is always advised to choose the 2theta angles near around the standard's peaks (25-35 deg) for crystallite size calculation. Some time your instrument technician will let you know the instrumental contribution to broadening.