Homework 6
(Problems)
 Problems 6.1, 6.2 & 6.4 of Bergeron
and Risbud’s book
 Problem 1 (a-i) of Part I, Hummel’s
book, p. 263
6.1. For Fig. 6.72.
a. Label primary phase
fields.
b. Construct Alkemade
lines.
c. Indicate slopes of
boundary lines.
Fig. 6.72. Illustrations
for problem 6.1.
6.2. For Fig. 6.73.
a. Make an isoplethal study
for a melt of composition
A=30%, B=5%, C=65%.
b. Make a sketch of the
isothermal section at
1100°C and at 700°C.
c. Make a sketch to represent
the vertical section taken
along a line from C to 80%
B (on the line AB).
6.4. For Fig. 6.74.
a. Make isoplethal studies for
melts of the following
compositions:
Melt 1: K=35%, G=60%, R=5%
Melt 2: K=10%, G=20%,
R=70%
b. Construct phase analysis
diagrams for the
compositions listed in part (a).
1.(a-i). For Diagram P5.1.
a. For a composition containing 80% C, 10% A and 10% B, trace the
crystallization path, making sure to describe ALL major events
as the liquid cools below the temperature of the invariant point
b. Show QUANTITATIVELY by calculation that one phase
partially dissolves at the invariant point as heat is withdrawn
from the system
c. Show that the amount of A, B and C in the final crystallized
mixture is the same as that in the original liquid (80C, 10A, 10B)
d. Trace the crystallization path of a composition containing 75%
C, 15% A and 10% B. The composition is on the join AC-BC. Make
a quantitative calculation just before and just after final
crystallization to show exactly what takes place at the invariant
point
1.(a-i). For Diagram P5.1.
e.
Trace the crystallization path of a liquid containing 65% C,
20% A, and 15% B on the boundary line between the primary
fields of C and BC
f.
How much solid and how much liquid coexist when the liquid
composition is 60% C, 30% A, and 10% B? What is the
composition of the solid?
g.
Make a construction which shows area starting liquids in the
primary field of BC as they proceed to the eutectic where AC,
BC and A coexist
1.(a-i). For Diagram P5.1.
h. For the liquid composition given in (e) above, make a
quantitative analysis of the equilibrium just before and just
after final crystallization at the eutectic. Show that the
amount of A, B and C in the assemblage of liquid, AC and BC
just before final crystallization is the same as that in the
starting liquid (65C, 20A, 15B). Show that the amount of A, B
and C in the final crystallized mixture of A, AC and BC is the
same as that in the starting liquid (65C, 20A, 15B). How much
A is precipitated during final crystallization at the invariant
point?
1.(a-i). For Diagram P5.1.
i.
Trace the crystallization path of a liquid containing 70% C, 5%
A and 25% B. Be sure to describe ALL major events which
occur as the temperature is lowered below the invariant point.
Make quantitative calculations at temperatures where C is in
equilibrium which liquid, where C and BC are in equilibrium with
liquid, where only BC is in equilibrium with liquid, where BC and
A are in equilibrium with liquid and just before and just after
final crystallization at the invariant point. How much B is
precipitated during reaction at the invariant point?
1.(a-i). For Diagram P5.1.