Answer:
For differents τ:
τ = 1000 Å → B = 0.11°
τ = 750 Å → B = 0.15°
τ = 250 Å → B = 0.44°
For differents Θ:
Θ = 10° → B = 0.31°
Θ = 45° → B = 0.44°
Θ = 80° → B = 1.78°
Explanation:
To factor B is related to the size of particles, Θ, and λ by the Scherrer equation:
[tex] \tau = \frac{K \lambda}{ B cos(\theta)} [/tex]
where τ: size of the particles, λ: is the wavelenght of the X-Rays, B: is the line broadening at half the maximum intensity, Θ: angle of incidence and K: is a shape factor with typical value of 0.9
[tex] B = \frac{K \lambda}{ \tau cos(\theta)} [/tex]
Now, factor B for the diameter of the particles (τ) is:
τ = 1000 Å:
[tex] B = \frac{0.9 \cdot 1.5}{1000 \cdot cos(45)} = 1.91\cdot 10^{-3} rad = 0.109 ^{\circ} [/tex]
τ = 750 Å:
[tex] B = \frac{0.9 \cdot 1.5}{750 \cdot cos(45)} = 2.54\cdot 10^{-3} rad = 0.146 ^{\circ} [/tex]
τ = 250 Å:
[tex] B = \frac{0.9 \cdot 1.5}{250 \cdot cos(45)} = 7.64\cdot 10^{-3} rad = 0.438 ^{\circ} [/tex]
For τ = 250 Å, factor B for angles of incidence is:
Θ = 10°:
[tex] B = \frac{0.9 \cdot 1.5}{250 \cdot cos(10)} = 5.48 \cdot 10^{-3} rad = 0.314 ^{\circ} [/tex]
Θ = 45°:
B = 0.438°
Θ = 80°:
[tex] B = \frac{0.9 \cdot 1.5}{250 \cdot cos(80)} = 0.031 rad = 1.78 ^{\circ} [/tex]
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