we use scherrer formula for analysis of Crystal material.
But for amorphous and semi crystalline material is the same is true? Because peak becomes broader and broader and scherrer formula gives 0.00x value also.
So what should be the right way to go?
The Scherrer equation gives you an estimate on the crystallite size normal to a specific lattice plane. Its analysis is based on the following thoughts:
Mathematically speaking a finite sized crystal can be thought of as the product of an infinite crystal multiplied by a finite box shaped function. As the diffraction pattern is the Fourier transform of the crystal, the product becomes a convolution of the infinite crystal(==the reciprocal lattice) with the Fourier transform of the shape function. With decreasing size the of the box in direct space, the width of the Fourier transform in reciprocal space widens.
As a last step this has to be projected from reciprocal space into the powder pattern to give the Scherrer equation.
In a truly amorphous material this thought process is no longer valid, as you do not have a finite object but a continuous (theoretically infinitely large) object, just without any translational long range order. For an amorphous material the analysis of the width of the first sharp diffraction peak via the Scherrrer will not give you any physically meaningful data.
What do you mean with "semi crystalline" material? Nanoparticles or a "glassy" substance with different width of the first sharp diffraction peak?
For a full analysis and understanding of the short range order in an amorphous or extremely ill ordered material an analysis with a Reverse-Monte-Carlo algorithm is best, see the many papers that cite Pusztai and McGreevy, for a good start see
https://en.wikipedia.org/wiki/Reverse_Monte_Carlo
If your "semi crystalline" materials are Nanoparticles, the Scherrer equation gives reasonable estimates of the crystallite size down to some 4 nm. A full analysis would best be performed by a full structure simulation and calculation of the nanoparticle's powder pattern via the Debye Scattering Equation. For softwre look at Antonio Cervellinos Debussy or my DISCUS_SUITE
https://github.com/tproffen/DiffuseCode
The term "semi-crystalline" typically refers to a material with amorphous and crystalline regions, such as is common in polymers. Is that what you mean? The XRD pattern would have sharp crystalline peaks superimposed on a broad amorphous background.
Or do you mean poorly crystallized? Oh, wait, that is unclear too. Do you mean crystallzied with lots of defects?
If the material is amorphous or poorly crystalline then it has got no crystallite diameter. In this case, it is meaningless to use the Sharrer equation!
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