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Reading: Required: Allen Chapter 15, pp 317-331 Supplemental Reading: Tinoco (5 th Ed) pp 574-597 Assigned Problems: - Problems discussed in class - Posted problems X-ray crystallography

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a. X-rays with wavelength 1.54 Å are used to collect diffraction data on a crystal. Calculate the angle at which the reflection (diffraction peak) for Miller planes with d = 3.00 Å is observed. Bragg’s Law (1) 1. 𝝑 = 14.9° 2. 𝝑 = 0.257° 3. 𝝑 = 0.513° 4. 𝝑 = 57.4° 5. 𝝑 = 30.9°
a. X-rays with wavelength 1.54 Å are used to collect diffraction data on a crystal. Calculate the angle at which the reflection (diffraction peak) for Miller planes with d = 3.00 Å is observed. Bragg’s Law (1) 2 d 𝐬𝐢𝐧 𝝑 = 𝒏𝝀; 𝒏 = ?; 𝒔𝒊𝒏 𝝑 = ?.?? Å ? × ?.?? Å 𝒔𝒊𝒏 𝝑 = 0.257; 𝝑 = 14.9° Answer: 1. 14.9°

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b. X-rays with wavelength 1.54 Å are used to collect diffraction data on a crystal. Calculate the angle at which the reflection (diffraction peak) for Miller planes with d = 1.50 Å is observed. Bragg’s Law (2) 1. 𝝑 = 14.9° 2. 𝝑 = 0.257° 3. 𝝑 = 0.513° 4. 𝝑 = 57.4° 5. 𝝑 = 30.9°
b. X-rays with wavelength 1.54 Å are used to collect diffraction data on a crystal. Calculate the angle at which the reflection (diffraction peak) for Miller planes with d = 1.50 Å is observed. Bragg’s Law (2) 2 d 𝐬𝐢𝐧 𝝑 = 𝒏𝝀; 𝒏 = ?; 𝒔𝒊𝒏 𝝑 = ?.?? Å ? ×?.?? Å 𝒔𝒊𝒏 𝝑 = 0.513; 𝝑 = 30.9° Answer: 5. 𝝑 = 30.9°

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Bragg’s Law (3) c. Which set of Miller planes provides higher-resolution information? 1. the set with d = 3.0 Å 2. the set with d = 1.5 Å 3. They provide the same resolution. 4. Cannot be determined.
Bragg’s Law (3) c. Which set of Miller planes provides higher-resolution information? 2. The set with d = 1.5 Å provides higher resolution data. Answer:

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Bragg’s Law (4) d. X-rays with wavelength 1.54 Å are used to collect diffraction data on a crystal. What is the theoretical resolution limit for this experiment? 1. 1.54 Å 2. 3.08 Å 3. 0.77 Å 4. 0.649 Å -1 5. 1.30 pm 6. 0.77 nm
Bragg’s Law (4) d. X-rays with wavelength 1.54 Å are used to collect diffraction data on a crystal. What is the theoretical resolution limit for this experiment? Answer: 3. 0.77 Å

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Miller Planes (1) What are the hkl Miller indices for the set of Miller planes shown below? 1. (hkl) = (220) 2. (hkl) = (330) 3. (hkl) = (111) 4. (hkl) = (1, -1, 0) 5. (hkl) = (000)
Miller Planes (1) What are the hkl Miller indices for the set of Miller planes shown below? Answer: 4. (hkl) = (1, -1, 0)

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Miller Planes (2) What are the hkl indices for the set of Miller planes shown below?
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