Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-10 GTBL042-Callister-v2 August 13, 2007 18:16

Questions and Problems • 397

Congruent Phase Transformations

Binary Eutectic Systems

Equilibrium Diagrams Having Intermediate

Phases or Compounds

Eutectoid and Peritectic Reactions

10.24Figure 10.40 is the tin–gold phase diagram,

for which only single-phase regions are

labeled. Specify temperature–composition

points at which all eutectics, eutectoids, peri-

tectics, and congruent phase transformations

occur. Also, for each, write the reaction upon

cooling.

10.25Construct the hypothetical phase diagram for

metals A and B between room temperature

(20◦C) and 700◦C given the following infor-

mation:

• The melting temperature of metal A is
  480 ◦C.


• The maximum solubility of B in A is 4
  wt% B, which occurs at 420◦C.


• The solubility of B in A at room temper-
  ature is 0 wt% B.


• One eutectic occurs at 420◦C and 18 wt%
  B–82 wt% A.


• A second eutectic occurs at 475◦C and 42
  wt% B–58 wt% A.

(Sn) Composition (wt% Au) (Au)

Temperature (

°C)

020



  





40

L

60 80 100

200

400

600

800

1000

Figure 10.40 The tin–gold phase diagram.

(Adapted with permission fromMetals

Handbook,8th edition, Vol. 8,Metallography,

Structures and Phase Diagrams,American

Society for Metals, Metals Park, OH, 1973.)

• The intermetallic compound AB exists at
  a composition of 30 wt% B–70 wt% A,
  and melts congruently at 525◦C.


• The melting temperature of metal B is
  600 ◦C.


• The maximum solubility of A in B is 13
  wt% A, which occurs at 475◦C.


• The solubility of A in B at room temper-
  ature is 3 wt% A.

Ceramic Phase Diagrams

10.26From Figure 10.24, the phase diagram for the

MgO–Al 2 O 3 system, it may be noted that

the spinel solid solution exists over a range

of compositions, which means that it is non-

stoichiometric at compositions other than 50

mol% MgO–50 mol% Al 2 O 3.

(a)The maximum nonstoichiometry on the

Al 2 O 3 -rich side of the spinel phase field

exists at about 2000◦C (3630◦F) corre-

sponding to approximately 82 mol% (92

wt%) Al 2 O 3. Determine the type of va-

cancy defect that is produced and the

percentage of vacancies that exist at this

composition.

(b)The maximum nonstoichiometry on the

MgO-rich side of the spinel phase field