Abstract
After definition of the notion phase and component, the state of equilibrium is defined. The basic thermodynamic energy functions are introduced. Dynamic equilibria and stationary states are discussed and compared. Phase equilibria conditions are introduced. The determination of the number of independent intensive state variables, called the degrees of freedom, is described after derivation of Gibb’s phase rule. An extensive presentation of the topology of phase diagrams, of one component systems, and especially of binary and also ternary systems, is given in the order of increasing complexity. The relation with microstructure development upon phase transformation, as guessed from the phase diagram, is dealt. The chapter ends with a focus on rules and boundary conditions to be satisfied in the construction of phase diagrams from experimental data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The text presented in this paragraph is perhaps not easy to penetrate at first glance. However, much confusion occurs in the determination of n for cases (much) more complicated than as considered until now (i.e. as in Sect. 7.2). The above given, general formulation to determine the minimum number of necessary components, n, has been taken, practically one-to-one, from a literature source where a focus is on gas and gas–solid reactions (J.T. Slycke, E.J. Mittemeijer and M.A.J. Somers in E.J. Mittemeijer and M.A.J. Somers (Eds.), Thermochemical Surface Engineering of Steels, Elsevier (Woodhead), 2015, p. 18). In that work the general approach to determine n has to be followed and has been illustrated by a number of examples of variable, distinct complexity. The treatment in the present book, for the determination of n, deals with cases not more complicated than as discussed in Sect. 7.2.
- 2.
Homologous materials are materials of similar (chemical) structures and related physical properties, as in the present case ∆Hf through Tm.
- 3.
At a number of places, in especially this chapter, for the purpose of illustration, phase diagrams of some binary systems are presented, which have been redrawn from the compilation provided by Massalski et al. (1996). The numerical composition and temperature data, as indicated for specific points/lines in these diagrams, have been adopted as given in this compilation. These numerical data, as presented in some cases, can suggest an accuracy, which from an experimental point of view, is surprisingly high. For example, see the Al-Si phase diagram shown in Fig. 7.12. The melting point of Al (at 1 atm) has been indicated as 660.452 °C. Such an indication implies that the true melting point of Al would likely be in the range 660.4515–660.4525 °C. An experimentalist knows that knowledge of the relative temperature in an experiment with a precision of 0.01 °C (0.01 K) is already a very good achievement. Apart from the melting points of the pure elements, the numerical values given in these phase diagrams can be based on the outcome of a computational model description/evaluation of the thermodynamics of the system, indeed derived from experimental data, but the significance of the computed/evaluated values can never be better than the inaccuracy corresponding with the experimental errors inherent in the data used, although a computer can produce a practically endless list of decimals.
- 4.
The Fe–C phase diagram is of great practical importance (steels!). It returns at a number of places in this book in different fashions: Fig. 7.22b, Fig. 9.9, Fig. 9.22a (based on the same literature source as for Fig. 7.22b, but differently presented; see what follows), and finally Fig. 9.24 (the latest version). Thereby the ongoing efforts to determine and understand the underlying thermodynamics of the Fe–C phase diagram are illustrated. Also see the “Intermezzo: The Fe–C and Fe–N phase diagrams” at the end of Sect. 9.5.2.1.
Finally it is recalled that in phase–diagram drawings the composition parameter along the abscissa at the bottom of the figure usually is “the more fundamental, linearly presented atom-fraction (-percentage)”, whereas, simultaneously, the weight(mass) fraction is usually shown, then not linearly, along the abscissa at the top of the figure [see below Eq. (7.13) in Sect. 7.5.2]. However, in case of Figs. 9.9 and 9.22a reverse policy has been followed: the, then linearly presented, weight(mass)-fraction scale has been placed at the bottom of the Fe–C phase diagram. This reflects the preferred use by engineers in industrial practice of weight(mass) fractions (e.g. in the steel making process).
References
General
Y.A. Chang, Phase diagram calculations in teaching, research and industry. Metall. Mater. Trans. A 37A, 273–305 (2006)
S. Lele, Phase diagrams—Past Present and Future. IIM Metal News 14, 22–41 (2011)
H.L. Lukas, G.S. Fries, B. Sundman, Computational Thermodynamics (Cambridge University Press, Cambridge, 2007).
T.B. Massalski (ed.), Binary Alloy Phase Diagrams, 2nd edn. (ASM, Metals Park Ohio, 1996)
B. Predel, M. Hoch, M. Pool, Phase Diagrams and Heterogeneous Equilibria (Springer, Berlin, 2004).
N. Saunders, P.A. Miodownik, CALPHAD Calculation of Phase Diagrams (Pergamon Press, Oxford, 1998).
G. Petzow, G. Effenberg (eds.), Ternary Alloys: A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams (Wiley-VCH Verlag, Weinheim) (a series of volumes published starting 1988)
Specific
S.-L. Chen, R. Schmid-Fetzer, K.-C. Chou, Y. Austin Chang, W.A. Oates, A note on the application of the phase rule. Int. J. Mater. Res. 99, 1210–1212 (2008)
E.J. Mittemeijer, M.A.J. Somers, Thermodynamics, kinetics, and process control of nitriding. Surf. Eng. 13, 483–497 (1997)
S. Sommadossi, W. Gust, E.J. Mittemeijer, Characterization of the reaction process in diffusion-soldered Cu/In-48 at.% Sn/Cu joints. Mater. Chem. Phys. 77, 924–929 (2002)
F. Spaepen, A survey of energies in materials science. Phil. Mag. 85, 2979–2987 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mittemeijer, E.J. (2021). Phase Equilibria. In: Fundamentals of Materials Science. Springer, Cham. https://doi.org/10.1007/978-3-030-60056-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-60056-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-60055-6
Online ISBN: 978-3-030-60056-3
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)