School of Mechanical and Mining Engineering

MATE7014: Advanced Materials Characterisation

Problem Based Learning 1: Crystal Structure (weight 5% of the total mark)

(Date: 9/8/2024; Time: 12:00 – 14:50; Venue: 09-201)

(Submission by 14:50 on this date via TurnItIn)

1. Figure 1 below schematically shows the three crystal lattices of metals (unit cells), body centered cubic (BCC), face centered cubic (FCC) and hexagonal close packed (HCP). Specify the indices (Miller-Bravais indices for HCP) of the directions (marked with the blue lines) and planes (marked by the red lines) marked in the unit cells. (BCC: 6 marks; FCC: 6 marks; HCP: 8 marks) (Use the letters to denote the directions and planes, such as direction AC, plane FEG and etc.).  (20 marks)

Figure 1  Schematic illustration of the three crystal structures of metals.  (a) BCC; (b) FCC; and (c) HCP. (For Question 1)

2. Calculate the interplanar spacing (d-value) of (112) and (121) crystal planes of cementite (an iron carbide, Fe₃C), i.e. d₁₁₂ and d₁₂₁ (Cementite has an orthorhombic lattice structure with the lattice parameters a = 0.45241nm, b = 0.50883nm, c = 0.67416nm). Are these two planes in the same plane family? (10 marks)

3. Calculate the interplanar spacing (d-value) of (112) and (121) crystal planes of pure copper, i.e. d₁₁₂ and d₁₂₁ (Cu has an FCC structure with the lattice parameter a = 0.3649 nm).  Are these two planes in the same plane family? Comparing with the calculated results in Question 2, what is the difference in the d-values of the two planes between cementite and pure Cu in addition to the different actual values? (10 marks)

4. Which three of the following five crystal planes are in the same zone (they share the same zone axis) in orthorhombic lattice. (10 marks). What is the actual zone axis? (5 marks)

(212), (111), (431), (311), (115)

5. List all equivalent directions in a <310> family in a cubic system? (10 marks)

6. Is [132] direction normal to (perpendicular to) (132) plane in an orthorhombic lattice structure? Is [123] direction normal to (123) plane in a cubic lattice? (10 marks)

7. For an orthorhombic structure, it has been determined that d₀₀₂ = 0.468 nm, d₁₀₁ = 0.347 nm, and d₁₁₂ = 0.208 nm. Using this information to determine its lattice parameters. (10 marks)

8. In an orthorhombic structure with lattice parameter a = 0.5 nm, b = 0.6 nm and c = 0.7 nm, calculate the angle between the (112) plane and the (112) plane, and the angle between the [112] direction and the [231] direction. (10 marks)

9. In a cubic lattice structure, which two in the following directions are in the (123) plane? (5 marks)

[011], [111], [211],[032], [132].