Page 329 - Materials Science and Engineering An Introduction

9.6 One-Component (or Unary) Phase Diagrams • 301

equilibrium is reflected by a constancy with time in the phase characteristics of a system.
Perhaps an example best illustrates this concept. Suppose that a sugar–water syrup is
contained in a closed vessel and the solution is in contact with solid sugar at 20 C. If the
system is at equilibrium, the composition of the syrup is 65 wt% C 12 H 22 O 11 –35 wt% H 2 O
(Figure 9.1), and the amounts and compositions of the syrup and solid sugar will remain
constant with time. If the temperature of the system is suddenly raised—say, to 100 C—
this equilibrium or balance is temporarily upset and the solubility limit is increased to
80 wt% C 12 H 22 O 11 (Figure 9.1). Thus, some of the solid sugar will go into solution in the
syrup. This will continue until the new equilibrium syrup concentration is established at
the higher temperature.
This sugar–syrup example illustrates the principle of phase equilibrium using a
liquid–solid system. In many metallurgical and materials systems of interest, phase equi-
librium involves just solid phases. In this regard the state of the system is reflected in
the characteristics of the microstructure, which necessarily include not only the phases
present and their compositions, but, in addition, the relative phase amounts and their
spatial arrangement or distribution.
Free energy considerations and diagrams similar to Figure 9.1 provide information
about the equilibrium characteristics of a particular system, which is important, but
they do not indicate the time period necessary for the attainment of a new equilibrium
state. It is often the case, especially in solid systems, that a state of equilibrium is never
completely achieved because the rate of approach to equilibrium is extremely slow; such
metastable a system is said to be in a nonequilibrium or metastable state. A metastable state or
microstructure may persist indefinitely, experiencing only extremely slight and almost
imperceptible changes as time progresses. Often, metastable structures are of more
practical significance than equilibrium ones. For example, some steel and aluminum
alloys rely for their strength on the development of metastable microstructures during
carefully designed heat treatments (Sections 10.5 and 11.9).
Thus it is important to understand not only equilibrium states and structures, but
also the speed or rate at which they are established and the factors that affect that rate.
This chapter is devoted almost exclusively to equilibrium structures; the treatment of
reaction rates and nonequilibrium structures is deferred to Chapter 10 and Section 11.9.

Concept Check 9.1 What is the difference between the states of phase equilibrium and
metastability?
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]

9.6 ONE-COMPONENT (OR UNARY)
PHASE DIAGRAMS
Much of the information about the control of the phase structure of a particular system is
phase diagram conveniently and concisely displayed in what is called a phase diagram, also often termed an
equilibrium diagram. Three externally controllable parameters that affect phase structure—
temperature, pressure, and composition—and phase diagrams are constructed when various
combinations of these parameters are plotted against one another.
Perhaps the simplest and easiest type of phase diagram to understand is that for a
one-component system, in which composition is held constant (i.e., the phase diagram
is for a pure substance); this means that pressure and temperature are the variables.
This one-component phase diagram (or unary phase diagram, sometimes also called
a pressure–temperature [or P–T] diagram) is represented as a two-dimensional plot of