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## Boris S. Bokstein, Mikhail I. Mendelev, and David J. Srolovitz

Print publication date: 2005

Print ISBN-13: 9780198528036

Published to Oxford Scholarship Online:

DOI: 10.1093/oso/9780198528036.001.0001

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# Phase equilibria I

Chapter:
(p.35) 2 Phase equilibria I
Source:
Thermodynamics and Kinetics in Materials Science
Publisher:
Oxford University Press
DOI:10.1093/oso/9780198528036.003.0004

This chapter addresses the general features of phase equilibria and applies them to single component systems. Before extending our study of phase equilibria to the interesting case of multiphase, multicomponent systems, we examine the special case of single phase, two-component systems (Chapter 3). Phase equilibria in multiphase, multicomponent systems is deferred until Chapter 4. A single substance may exist in different states. For example, H2O can exist as water vapor, liquid water, or any one of several solid phases (ices). Different states can co-exist indefinitely under certain sets of conditions. Under such conditions, the co-existence of these states suggests that they are in equilibrium with respect to one another, that is, phase equilibrium has been established. It is convenient to graphically represent phase equilibria in the form of phase diagrams. An example of such a diagram for a one-component system (with no solid state allotropes) is shown in Fig. 2.1. The AO, OB, and OC lines represent conditions for which two phases are in equilibrium. Since each set of two-phase equilibrium is represented by a one-dimensional surface (i.e. a line), we see that we can vary one parameter (either T or p) without entering a one-phase region of the diagram. For example, if we set the temperature to T1 we can find a saturated vapour pressure p1 such that the liquid and gas co-exist. Three phases simultaneously co-exist at point O, which is called the triple point. Since the three-phase co-existence surface is zero dimensional (i.e. a point), three-phase equilibrium only exists at a specific temperature and pressure, that is, no conditions can be varied. On the other hand, every single-phase region of the diagram is a two-dimensional area and, hence, we can simultaneously, vary two parameters (i.e. both the temperature and pressure) and still remain in the same single-phase region of the diagram. Equations describing the lines of phase equilibria will be derived in Section 2.2, below. Unlike the lines describing the solid–liquid or solid–vapor co-existence, the liquid–vapor co-existence line terminates in a single-phase region of the diagram.

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