ENGINEERING TRIPOS
SECOND YEAR
Part IB Paper 3: MATERIALS
SOLUTIONS to Examples Paper 1: TEACH YOURSELF PHASE DIAGRAMS
PART 4: Interpreting more Complex Phase Diagrams
12.
Figure 6: Al-Si and Cr-Ni phase diagrams
o
Al-Si: eutectic at 580 C, composition 12wt% Si.
Cr-Ni: eutectic at 1350oC, composition 47at% Ni.
Conversion to wt%: wt% Ni = (0.4758.71)/(0.5352.0 + 0.4758.71) = 50.0 wt% Ni
13.
(i) 70/30 brass is single-phase, but 60/40 brass
is two-phase.
(ii) 70/30 brass starts to melt at 920oC and is
completely liquid at 960oC.
(iii) At 200oC:  (copper-rich solid) and 
(roughly CuZn). WZn ≈ 33%, WZn ≈ 48%.
Proportions roughly 50-50; more precisely:
proportion of  = (48-40)/(48-33) = 53%, and
47% .
Figure 7: Cu-Zn phase diagram
14. (a,b)
Eutectoids:
1. WZn = 24wt%, T = 586oC
2. WZn = 35wt%, T = 580oC
3. WZn = 28wt%, T = 520oC
4. WZn = 32wt%, T = 350oC
Figure 8: Cu-Sn phase diagram
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ENGINEERING TRIPOS
SECOND YEAR
15. (a,b) See Figure 9. Compounds at
approx. 53, 59 and 62 wt% Al: call these
TiAlx , TiAly , and TiAlz.
(i) wt% Al  0.53 = 26.98x/(47.9+26.98x).
Solving for x: x (1–0.53)26.98 = 0.5347.9
Hence x  2.0. Compound therefore TiAl2.
(ii) wt% Al  0.59 = 26.98y/(47.9+26.98y).
Solving for y: y (1–0.59)26.98 = 0.5947.9
Hence y  2.55. Compound therefore Ti2Al5.
(iii) wt% Al  0.62 = 26.98z/(47.9+26.98z).
Solving for z: z (1–0.62)26.98 = 0.6247.9
Hence z  2.9. Compound therefore TiAl3.
(c) Ti-6wt% Al: transformation from to 
from approx. 980 – 1010oC; melting from
approx. 1650 – 1660oC.
Figure 9: Ti-Al phase diagram
16. (a) Mullite contains approximately 73wt% Al2O3 (27% SiO2).
The molecular weight of SiO2 is 28.1 + (16  2) = 60.1
The molecular weight of Al2O3 is (26.9  2) + (16  3) = 101.8
Molecular weight of mullite = 1 mol of SiO2 + x mols of Al2O3 = 60.1 + 101.8x
Alumina fraction by weight  0.73  101.8x/(60.1 + 101.8x)
Hence x  1.6.
(b) At 1700oC and 50wt% Al2O3, the phases
are liquid containing 13 wt% Al2O3 and
mullite containing 71 wt% Al2O3.
Weight fraction of liquid =
(71-50)/(71-13) = 36%
Weight fraction of mullite =
(50-13)/(71-13) = 64%.
It would be valid to measure the lengths
of the tie-line directly in this case
because the phase diagram has a linear
weight % scale.
Figure 10: SiO2-Al2O3 phase diagram
H.R. Shercliff
G.J. McShane
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