Question

A crystal has a cubic unit cell of 4.2 Å. Using a wavelength of 1.54 Å at what angle (2
)
would you expect to measure the (111) peak

Answer 1

Question #54027, Physics / Solid State Physics

A crystal has a cubic unit cell of 4.2 Å. Using a wavelength of 1.54 Å at what angle (2) would you expect to measure the (111) peak

Solution:

d-spacing for a cubic cell is defined:

$1 / \mathrm{d}^{2} = (\mathrm{h}^{2} + \mathrm{k}^{2} + \mathrm{l}^{2}) / \mathrm{a}^{2}$ , where a -the unite cell parameter, d - the separation between lattices.

$1 / \mathrm{d}^{2} = (3) / 17.64 \times 10^{-20} \mathrm{~m}^{2} = 0.170068 \times 10^{20} \mathrm{~m}^{2}$

$\mathrm{d} = 2.4249 \times 10^{-10} \mathrm{~m}$

According to Brag condition the wavelength can be found:

$2\mathrm{d}\sin (\Theta) = n\lambda$ , where $\Theta$ - the angle to measure the (111) peak, and $\lambda$ - the wavelength of X-ray.

$\sin (\Theta) = 1.54 \times 10^{-10} \mathrm{~m} / (2 \times 2.4249 \times 10^{-10} \mathrm{~m}) = 0.3175$

$\Theta = \arcsin (0.3175) = 18.5{}^{\circ}$

Answer:

$\Theta = \arcsin (0.3175) = 18.5{}^{\circ}$

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