The fullwidth at half of Imax of AB2 powder is 0,2° at 2θ=32°. Please calculate the crystal size of the sample. (Cu Ka = 1,541 A)
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To calculate the crystal size of the sample, we need to use the Scherrer equation. The Scherrer equation relates the crystal size with the full width at half maximum (FWHM) of the X-ray diffraction peak.
The Scherrer equation is given by:
D = Kλ / (β⋅cosθ)
Where:
D is the average crystal size
K is the Scherrer constant (typically taken as 0.89)
λ is the wavelength of the X-ray radiation (given as Cu Ka = 1.541 Å)
β is the FWHM of the X-ray diffraction peak
θ is the Bragg angle
In this case, we are given the FWHM (fullwidth at half of Imax) as 0.2° at 2θ = 32°.
First, we need to convert the given angle to the Bragg angle by dividing it by 2:
θ = 32° / 2
θ = 16°
Now, let's substitute the known values into the Scherrer equation:
D = 0.89 × 1.541 Å / (0.2° × cos(16°))
To perform the calculation, we need to convert the angle from degrees to radians. The equation will be:
D = 0.89 × 1.541 Å / (0.2° × cos(16° × (π/180)))
Now we can evaluate the equation:
D = 0.89 × 1.541 Å / (0.2° × cos(0.2793))
Using a scientific calculator, we can find:
D ≈ 18.4 Å
Therefore, the crystal size of the sample is approximately 18.4 Å.