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b. Show QUANTITATIVELY by calculation that one phase partially dissolves at the invariant point as heat is withdrawn from the system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.