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Nuclear Engineering 265

Introduction to Materials for Nuclear Applications

Homework 3 Due September 21, 2017

10 Points Each

1) Within a cubic unit cell, sketch the following directions: [011], [10 2 ], [3 1 1], [ 2 12], and [ 1 01] Hint: It would be easier for the grader if you draw 5 different cells so that your direction diagrams are clearly understandable.

2) Within a cubic unit cell, sketch the following planes: (011), (10 2 ), (3 1 1), ( 2 12), and ( 1 01) Hint: It would be easier for the grader if you draw 5 different cells so that your direction diagrams are clearly understandable.

3) Determine the indices for the directions shown in the following cubic unit cell:

For the grader: Show the steps to go from points to direction. Do not just write the answer!

Nuclear Engineering 265

Introduction to Materials for Nuclear Applications

4) Determine the Miller indices for the planes shown in the following unit cells:

For the grader: Show the steps to go from intercepts to plane. Do not just write the answer!

5) Sketch the [11 2 0] and [1101] directions in a hexagonal unit cell. (As stated in class – you need to work with this in HW, but not for exam)

6) Sketch the (2110) and (1010) planes in a hexagonal unit cell. (As stated in class – you need to work with this in HW, but not for exam)

7) Linear Density a) Derive linear density expressions in terms of the atomic radius R for the [100], [110], and [111] directions in a metallic FCC crystal. b) If this FCC metal is copper, compute the linear density values for these directions. Which direction has the highest linear density? Why? 8) Planar Density a) Derive planar density expressions in terms of the atomic radius R for the (100) and (110) planes in a metallic BCC crystal. b) If this BCC metal is molybdenum, compute the planar density values for these planes. Which plane has the highest planar density? Why? 9) Determine the expected diffraction angle 2 for the first-order reflection from the (310) set of planes for BCC chromium when monochromatic radiation of wavelength 0.0711 nm is used. 10) The metal niobium has a BCC crystal structure. If the angle of diffraction for the (211) set of planes occurs at 2 = 75.99° (first-order reflection) when monochromatic xradiation having a wavelength of 0.1659 nm is used, compute the following: a) The interplanar spacing for this set of planes (d211) b) The atomic radius for the niobium atom (starting from the data you have)....