Alloys
Matter is known to occur in three different states as gas, liquid, or solid. Each element has a specific melting temperature T m , which separates the solid and liquid temperature regimes and a boiling temperature T b ,for the transition from liquid to ga
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Alloys
4.1 Constitution of Alloys Matter is known to occur in three different states as gas, liquid, or solid. Each element has a specific melting temperature Tm, which separates the solid and liquid temperature regimes and a boiling temperature for the transition from liquid to gas. At Tm and two states of matter are in thermodynamic equilibrium. Melting and boiling temperatures also depend on pressure p, although this dependency may be very mild as in metals. Accordingly, the existence of a state (phase) is represented by a certain range in the p-T diagram (Fig. 4.1). The lines in this diagram separate the ranges of existence of two phases and define the conditions where these two phases are in equilibrium. At the triple point all three phases are in equilibrium with each other. Between the triple point and the critical point (cr.P.), the transition from the liquid to the vapor phase is discontinuous. Beyond this critical point the phase transition from liquid to gas proceeds continuously. For a given pressure there is a defined melting temperature and a defined boiling temperature, namely the points of intersections of the respective isobar (line of constant pressure) and the phase boundaries of the phase diagram (Fig. 4.1). The range of existence of phases in thermal equilibrium follows Gibbs phase rule
n
f=n-P+2
n,
(4.1a)
where n is the number of components, P the number of phases, and f the number of degrees of freedom. The components are the building blocks of the system, for instance the kinds of atoms in case of elements and their mixtures, or stable chemical compounds in more complex systems. For a pure element n = 1. A phase is a physically unique s11hstance, not necessarily of constant chemical composition, for instance in a solid solution the composition maybe different. In a multicomponent system additional phases can occur by chemical reactions. The number of degrees of freedom denotes the number of
G. Gottstein, Physical Foundations of Materials Science © Springer-Verlag Berlin Heidelberg 2004
108
4 Alloys
variables in the system, that under the given conditions can be changed. In a one-component system (n = 1) the Gibbs phase rule means that, in the range of a single phase (P = 1), two parameters can be changed, namely pressure and temperature. At the triple point, however, P = 3 and f = 0, i.e. only at these specific values of pressure and temperature can all three phases be in equilibrium with each other.
Cr.P.
p*
6.13
T.' 273.0075
Ca)
Cb)
Fig. 4.1. Phase diagrams of water (a) and carbon dioxide (b). For a given pressure p' there is a certain melting point T;;" and boiling point Tt. The decrease of T m. with increasing pressure is a characteristic property of water. TP = triple junction point, Cr.P. = critical point.
Since the melting temperature and boiling temperature of metals depend only very little on pressure, and since in most commercial applications the pressure is the ambient pressure and not subject to change, the Gibbs phase rule is commonly used in the form
f=n-P+1
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