Q: Given AgBr and AgCl both have the NaCl structure, which of the following is true about their X-ray diffraction patterns if $$a_{AgBr} = 5.7748$$ Å and $$a_{AgCl} = 5.5501$$ Å?

AgBr will have its diffraction peaks at lower $$2\theta$$ values compared to AgCl.

Question 1

Which of the following best describes the crystal structure shown in the first image (with $$a_0 = 0.357$ nm)?

Accepted Answer

Diamond cubic structure

Question 2

Given a BCC iron (Fe) crystal with atomic radius $$r = 0.1241 nm $$and X-ray wavelength $$\lambda = 0.0711 nm$$, which set of Miller indices $$(hkl)$$ will produce a first-order diffraction peak at $$2	heta = 46.21^\circ$$?

Accepted Answer

$$(110)$$

Question 3

For a BCC metal with lattice parameter $$a = 0.33 nm $$and X-ray wavelength $$\lambda = 0.1541 nm$$, which of the following planes will NOT produce an observable diffraction peak?

Accepted Answer

$$(210)$$

Question 4

Using Bragg's Law $$n\lambda = 2d\sin	heta$$, what is the value of $$d$$ for the $$(110)$$ plane in a BCC crystal with $$a = 0.33 nm$$?

Accepted Answer

$$d = \frac{a}{\sqrt{2}} = 0.233 nm$$

Question 5

A sample of chromium (Cr) is analyzed by X-ray diffraction using $$\lambda = 1.5418$$ Å and $$a = 2.96$$ Å. If the angle of reflection $$	heta = 31.4^\circ$$, what are the Miller indices $$(hkl) of $$the reflecting plane?

Accepted Answer

$$(110)$$

Question 6

Which of the following statements about the structure factor $$F_{hkl}$$ for the diamond structure is correct?

Accepted Answer

The structure factor is nonzero only when $$h, k, l$$ are all even or all odd.

Question 7

Given AgBr and AgCl both have the NaCl structure, which of the following is true about their X-ray diffraction patterns if $$a_{AgBr} = 5.7748$$ Å and $$a_{AgCl} = 5.5501$$ Å?

Accepted Answer

AgBr will have its diffraction peaks at lower $$2	heta$$ values compared to AgCl.

Question 8

For a cubic crystal, the interplanar spacing $$d_{hkl} is $$given by which formula?

Accepted Answer

$$d_{hkl} = \frac{a}{\sqrt{h^2$ + k^2$ + l^2$}}$$

Question 9

Which of the following is a necessary condition for a diffraction peak to be observed in a BCC crystal?

Accepted Answer

$$h + k + l$$ must be even

Question 10

If the first four diffraction peaks for NaCl structure are to be calculated, which set of planes should be considered?

Accepted Answer

$$(200), (220), (222), (400)$$

Question 11

Which of the following best explains why the $$(100)$$ reflection is absent in the X-ray diffraction pattern of NaCl?

Accepted Answer

The structure factor for $$(100) is $$zero due to destructive interference between Na and Cl atoms.

Question 12

In the diamond structure, which atomic positions are occupied within the unit cell?

Accepted Answer

$$(0,0,0), (\frac{1}{2},0,\frac{1}{2}), (0,\frac{1}{2},\frac{1}{2}), (\frac{1}{2},\frac{1}{2},0), (\frac{1}{4},\frac{1}{4},\frac{1}{4}), (\frac{1}{4},\frac{3}{4},\frac{3}{4}), (\frac{3}{4},\frac{1}{4},\frac{3}{4}), (\frac{3}{4},\frac{3}{4},\frac{1}{4})$$

Question 13

Which of the following is the correct Bragg's Law equation for X-ray diffraction?

Accepted Answer

$$n\lambda = 2d\sin	heta$$

Question 14

If the X-ray wavelength is $$\lambda = 0.15418$$ Å and the lattice parameter for AgCl is $$a = 5.5501$$ Å, what is the $$2	heta$$ value for the $$(200)$$ peak?

Accepted Answer

$$2	heta = 16.0^\circ$$

Question 15

Which of the following is true about the ZnS (zinc blende) structure shown in the second image?

Accepted Answer

It is a face-centered cubic (FCC) lattice with Zn and S atoms occupying specific positions.

Solid State Physics: X-ray Diffraction and Crystal Structure Study Guide

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