X-ray diffraction method
It is an independent method to determine the amount of crystalline matter present in the fiber. W. L. Bragg presented a simple explanation of the diffracted beams from a crystal.
When X-ray beam is incident on a crystal, it strongly reflected wherever its layers of atoms at an angle show in fig. Such that, nλ=2dsinθ
n=1, 2, 3 . . . (order of diffraction)
λ= wave length of X‑rays.
d=distance between two atomic layers of crystal
θ=angle of incident radiation
From the figure we get,
∠BEC= ∠B’ EC=90⁰
∴∠DEC= ∠FEC= (90⁰- θ)
In ∆CDE, ∠CDE+∠DEC+∠DCE =180⁰
sin θ= DE/CE=DE/d
∴DE=d sin θ
In ∆EFC, ∠EFC+∠CEF+∠ECF =180⁰
sin θ=EF/CE =EF/d
∴EF= sin θ
So, the path difference between the two rays=DE+EF
= d sin θ +d sin θ
= 2d sin θ
Thus, for constructive interference,
2d sin θ=nλ
This equation is known as Bragg’s equation.
Advantages of X-ray diffraction method
⦿ It gives information about only crystallinity of a fiber.
⦿ It gives information about internal structure of the fiber.
⦿ It gives information about the shape of scattering particles.
⦿ It gives information about the distribution of spacing between the particles.
X-ray diffraction (XRD) spectrum of crystalline, semi-crystalline and amorphous polymer
Difference between IR method and X-ray method of fiber investigation