SS#______________________
Grade________/100
Metal 434
Final exam - 1994
1. (15) Give a complete, organized calculation of the value for c/a for an ideal A3 structure. Include lucid figures with figure titles. What is the value of c/a for an ideal A3 ' (alpha-La) structure? Why?
2. (10) Name all of the phase fields in this phase diagram. (not shown)
3. (10) alpha-uranium is Cmcm with a = 2.852, b = 5.865, c = 4.945 Å. Using the translucent paper and Wulff net supplied, draw a stereographic projection down the c axis which shows the exact positions of the {h00}, {0k0}, {00l}, {hk0}, {h0l}, and {0kl} poles. Start by sketching in the projection plane circle.
4. (15) Give the point group symbols in standard form for the three models being passed about. Yellow cards are not to be used.
no. ____ _________
no. ____ _________
no. ____ _________
1, 1-bar 2, m, 2/m , 222, mm2, 2/m2/m2/m , 4, 4-bar , 4/m , 422, 4mm, 4-bar 2m, 4/m2/m2/m , 23, 2/m3-bar , 432, 4-bar 3m, 4/m3-bar2/m , 3, 3-bar , 32, 3m, 3-bar2/m , 6, 6-bar, 6m , 622, 6mm, 6-bar 2m, 6/m2/m2/m
5. (10) With the aid of a drawing of the Debye-Scherrer camera geometry, rigorously derive the expression (which ignores the shrinkage correction):
S(mm)4 = theta(degrees)
6. (15) Write the BASIC statements which solve these three simultaneous equations for A1, A2, and A3 by Cramer's rule (determinants):
m1 A1 + m2 A2 + m3 A3 = v1
n1 A1 + n2 A2 + n3 A3 = v2
o1 A1 + o2 A2 + o3 A3 = v3
7. (15) Make a sketch below of the equilibrium microstructure of a 1020 steel which illustrates which microconstituents and roughly how much of each are present. Show the appropriate part of the phase diagram and discuss how you obtained your answer.
8. (10) Fe2P is P321 with a = 5.930, c = 3.453 Å, and FeI and
FeI in 3e, (x = 0.74) and 3f (x = 0.40), respectively, and PI and PII in
1b and 2d (z = 0.125), respectively. Draw the structure in projection down
the c axis, showing all the atoms in one unit cell. Identify each
type of atom and give the z coordinate of each.