Page 373 - Materials Science and Engineering An Introduction

Summary • 345

Phase Equilibria • A system at equilibrium is in its most stable state—that is, its phase characteristics do
not change over time. Thermodynamically, the condition for phase equilibrium is that
the free energy of a system is a minimum for some set combination of temperature,
pressure, and composition.
• Metastable systems are nonequilibrium ones that persist indefinitely and experience
imperceptible changes with time.

One-Component • For one-component phase diagrams, the logarithm of the pressure is plotted versus the
(or Unary) Phase temperature; solid-, liquid-, and vapor-phase regions are found on this type of diagram.
Diagrams
• For binary systems, temperature and composition are variables, whereas external
Binary Phase pressure is held constant. Areas, or phase regions, are defined on these temperature-
Diagrams versus-composition plots within which either one or two phases exist.

Binary Isomorphous • Isomorphous diagrams are those for which there is complete solubility in the solid
Systems phase; the copper–nickel system (Figure 9.3a) displays this behavior.

Interpretation of • For an alloy of specified composition at a known temperature and that is at equilib-
Phase Diagrams rium, the following may be determined:
What phase(s) is (are) present—from the location of the temperature–composition
point on the phase diagram.
Phase composition(s)—a horizontal tie line is used for the two-phase situation.
Phase mass fraction(s)—the lever rule [which uses tie-line segment lengths
(Equations 9.1 and 9.2)] is used in two-phase regions.

Binary Eutectic • In a eutectic reaction, as found in some alloy systems, a liquid phase transforms
Systems isothermally into two different solid phases upon cooling (i.e., L S a + b). Such a
reaction is noted on the copper–silver and lead–tin phase diagrams (Figures 9.7 and
9.8, respectively).
• The solubility limit at some temperature corresponds to the maximum concentration
of one component that will go into solution in a specific phase. For a binary eutectic
system, solubility limits are to be found along solidus and solvus phase boundaries.

Development of • The solidification of an alloy (liquid) of eutectic composition yields a microstructure
Microstructure in consisting of layers of the two solid phases that alternate.
Eutectic Alloys • A primary (or pre-eutectic) phase and the layered eutectic structure are the solidifica-
tion products for all compositions (other than the eutectic) that lie along the eutectic
isotherm.
• Mass fractions of the primary phase and eutectic microconstituent may be computed
using the lever rule and a tie line that extends to the eutectic composition (e.g.,
Equations 9.10 and 9.11).

Equilibrium • Other equilibrium diagrams are more complex, in that they may have phases/
Diagrams Having solid solutions/compounds that do not lie at the concentration (i.e., horizontal)
Intermediate Phases extremes on the diagram. These include intermediate solid solutions and interme-
or Compounds tallic compounds.
• In addition to the eutectic, other reactions involving three phases may occur at invari-
ant points on a phase diagram:
For a eutectoid reaction, upon cooling, one solid phase transforms into two other
solid phases (e.g., a S b + g).
For a peritectic reaction, upon cooling, a liquid and one solid phase transform
into another solid phase (e.g., L + a S b).