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

Answer on Question #51565, Physics, Solid State Physics

A crystal has a cubic unit cell of $4.2\,\mathrm{\AA}$. Using a wavelength of $1.54\,\mathrm{\AA}$ at what angle (2) would you expect to measure the (111) peak?

Solution

d-spacing equation for cubic is given by Eq.(1)

$$d = a / \sqrt{h^2 + k^2 + l^2} = a / \sqrt{l^2 + l^2 + l^2} = a / \sqrt{3}$$

According Bragg's law

$$2d \sin \theta = m\lambda$$

So, for

$$\theta = \arcsin\left(\frac{\lambda}{2d}\right) = \arcsin\left(\frac{\lambda\sqrt{3}}{2a}\right) = \arcsin\left(\frac{1.54\sqrt{3}}{2 \cdot 4.2}\right) \approx 18{}^{\circ}$$

Answer: $\theta \approx 18{}^{\circ}$

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