Page 374 - Materials Science and Engineering An Introduction

346 • Chapter 9 / Phase Diagrams

• A transformation in which there is no change in composition for the phases involved
is congruent.

The Gibbs Phase • The Gibbs phase rule is a simple equation (Equation 9.16 in its most general form)
Rule that relates the number of phases present in a system at equilibrium with the number
of degrees of freedom, the number of components, and the number of noncomposi-
tional variables.

The Iron–Iron • Important phases found on the iron–iron carbide phase diagram (Figure 9.24) are
Carbide (Fe–Fe 3 C) a-ferrite (BCC), g-austenite (FCC), and the intermetallic compound iron carbide [or
Phase Diagram cementite (Fe 3 C)].
• On the basis of composition, ferrous alloys fall into three classifications:
Irons (60.008 wt% C)
Steels (0.008 to 2.14 wt% C)
Cast irons (72.14 wt% C)

Development of • The development of microstructure for many iron–carbon alloys and steels depends
Microstructure in on a eutectoid reaction in which the austenite phase of composition 0.76 wt% C
Iron–Carbon Alloys transforms isothermally (at 727 C) into a-ferrite (0.022 wt% C) and cementite (i.e.,
g S a + Fe 3 C).
• The microstructural product of an iron–carbon alloy of eutectoid composition is
pearlite, a microconstituent consisting of alternating layers of ferrite and cementite.
• The microstructures of alloys having carbon contents less than the eutectoid (i.e., hy-
poeutectoid alloys) are composed of a proeutectoid ferrite phase in addition to pearlite.
• Pearlite and proeutectoid cementite constitute the microconstituents for hypereutec-
toid alloys—those with carbon contents in excess of the eutectoid composition.
• Mass fractions of a proeutectoid phase (ferrite or cementite) and pearlite may be
computed using the lever rule and a tie line that extends to the eutectoid composition
(0.76 wt% C) [e.g., Equations 9.20 and 9.21 (for hypoeutectoid alloys) and Equations
9.22 and 9.23 (for hypereutectoid alloys)].

Equation Summary

Equation Page
Number Equation Solving For Number

9.1b W L = C a - C 0 Mass fraction of liquid phase, binary isomorphous 306
C a - C L system

9.2b W a = C 0 - C L Mass fraction of a solid-solution phase, binary 306
C a - C L isomorphous system
9.5 V a = v a Volume fraction of a phase 308
v a + v b
W a
For a phase, conversion of mass fraction to 308
9.6a V a = r a volume fraction
W a W b
+
r a r b
9.7a W a = V a r a For a phase, conversion of volume fraction to 308
V a r a + V b r b mass fraction
(continued)