Calculate the breadth b ( in degrees of 2θ ), due to the small crystal effect alone, of the powder pattern lines of particles of diameter 1000, 750, and 250å. assume θ=45° and λ=1.5 å. for particles 250 å in diameter, calculate the breadth b for θ=10, 45, and 80°.

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:  

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      

Now, factor B for the diameter of the particles (τ) is:

τ = 1000 Å:          

τ = 750 Å:

τ = 250 Å:

For τ = 250 Å, factor B for angles of incidence is:  

Θ = 10°:

Θ = 45°:

B = 0.438°  

Θ = 80°:

Have a nice day!

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