Materials for engineering, 3rd Edition - (Malestrom)

220
Materials for engineering
Liquid
300
Temperature (°C)
200
α
19%
α + L
62%
180
β + L
98%
β
100
α + β
Fig. 7.1
20 40 60 80
Pb Wt% Sn
formed). The instantaneous concentration of the solid in contact with the
liquid phase, C x , may be expressed in terms of the fraction frozen, x:
C x = C 0 k(1 – x) k–1
where C 0 is the initial liquid concentration and k is the solid/liquid
distribution coefficient (i.e. the ratio of solute in the solid phase to that in
the liquid phase at a given temperature – it may be assumed to be constant).
Assuming that this equation applies to a casting, estimate the proportion
of non-equilibrium second phase which would occur in an alloy of Pb–
10 wt% Sn, the equilibrium diagram of which is shown above in Fig. 7.1.
[Answer: A fraction of 0.072]
5. With reference to the Ti–Ni equilibrium diagram reproduced below in
Fig. 7.2, discuss the reactions and the probable microstructures formed
when the following binary alloys of titanium are slowly cooled from
1600 to 800°C:
(a) 10 wt % nickel
(b) 50 wt % nickel
(c) 70 wt % nickel.
6. The molecular weight distribution was determined for a polyethylene
sample. The following number fractions (N i ) corresponding to particular
molecular weight ranges (M i ) were measured:
N i 0.26 0.31 0.21 0.13 0.07 0.015 0.001
M i 10 3 3 × 10 3 10 4 3 × 10 4 10 5 3 × 10 5 10 6
Calculate the number average molecular weight and the weight average
molecular weight for this polymer.