The basic phase diagrams
The reader is assumed to be familiar with the interpretation of binary phase diagrams and the chapter begins with a brief description of the specific features involved in the graphical representation of ternary and even higher order systems. Six ternary s
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4-1 Equilibria between condensed phases Basicrules Our knowledge of the metallurgy of steels, particularly as regards the effects of composition and temperature on microstructure, is largely based on experimental data obtained using a wide range of physical and chemical techniques. The thermodynamics of phase equilibria provides the only unifYing framework that enables these data to be compared and validated. When considering a particular system, a given quantity of matter is treated, that is a fixed total number of molecules (usually gram molecules or moles). The nature of the molecules is determined by the composition, i.e. by the concentrations of the different constituents, either elements or compounds. If a system comprises N constituents, the composition will be fully defined when N-I concentrations are fixed. The concentrations may be given in terms of atom or mole fractions or atomic or weight percentages. In practice, metallurgical phase diagrams are usually represented in terms of weight percentages. This approach will be applied in most of the diagrams considered, atomic percentages being used only when it is necessary to emphasize stoechiometric proporrions. 3. The majority of the calculations were performed using the Thermocalc or Pandat softwares, with data available in the SOTE bank in 2002.
M. Durand-Charre, Microstructure of Steels and Cast Irons © Springer-Verlag Berlin Heidelberg 2004
THE MICROSTRUC1URE OF STEELS ANO CAST IRONS The equilibrium conditions to which the system is subjected are described based on the first and second laws of chemica! thermodynamics. In particular, at equilibrium, the chemical potential of each constituent is identica! in each of the phases present. The equilibrium state is unique, that is, the number of phases, their proportions and their compositions are fixed. The phase eule was formulated by J.w. Gibbs in 1876. It stipulates the number of degrees of freedom F, or variance, in a system at equilibrium, i.e. the number of parameters that can vary independently, the variables in question being the temperature, the pressure and the concentrations of each of the constituents. For an alloy :
P+F=C+2
(4-1-1)
where P is the number of phases, C is the number of components and 2 represents the two variables pressure and temperature. In condensed metallic systems, pressure generally has very little influence in the rage of temperatures normally considered and is usually neglected, in which case the relation becomes P + F = C + 1. The phase transformations considered conserve the number of atoms of each species, and involve only their redistribution among the different phases. This forms the basis for the so-called "lever eule" in binary equilibria (cf § 5-1), which is a particular form of the barycentre rule for multicomponent systems.
Representations of phase equilibria The graphica! representations of phase equilibria are governed by the phase eule mentioned above. Thus, in a binary system (two constituents), an equilibrium between two phases will have only a single
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