CALPHAD

Many other parepistemes were stimulated by the new habits of precision in theory. Two important ones are the entropic theory of rubberlike elasticity in polymers, which again reached a degree of maturity in the middle of the century (Treloar 1951), and the calculation of phase diagrams (CALPHAD) on the basis of measurements of thermochemical quantities (heats of reaction, activity coefficients, etc.) here the first serious attempt, for the Ni-Cr Cu system, was done in the Netherlands by Meijering (1957). The early history of CALPHAD has recently been... 

Saunders, N. and Midownik, A.P. (1998) Calphad Calculation of Phase Diagrams (Pergamon Press, Oxford). 

As we have repeatedly seen in this chapter, proponents of computer simulation in materials science had a good deal of scepticism to overcome, from physicists in particular, in the early days. A striking example of sustained scepticism overcome, at length, by a resolute champion is to be found in the history of CALPHAD, an acronym denoting CALculation of PHAse Diagrams. The decisive champion was an American metallurgist, Larry Kaufman. 

Vol. 1 CALPHAD by N. Saunders and A. P. Miodownik Vol. 2 Non-Equilibrium Processing of Materials edited by C. Suryanarayana Vol. 3 Wettability at High Temperatures by N. Eustathopoulos, M. G. Nicholas and B. Drevet... 

I.54. K. Hack, T. Chart, paper presented at the IX CALPHAD Meeting Montreal, Canada, May 1980. 

L. Kaufman, B. Uhrenius, D. Birnie, K. Taylor, paper presented at the XII CALPHAD Meeting, Liege, Belgium, 29 Aug.-2 Sept., 1983. 

J.-M. Joubert, Crystal Chemistry and Calphad Modeling of the a Phase, Progress in Materials Science, Elsevier (2007). 

In order to examine the possible relationship between the bulk thermodynamics of binary transition metal-aluminum alloys and their tendency to form at underpotentials, the room-temperature free energies of several such alloys were calculated as a function of composition using the CALPHAD (CALculation of PHAse Diagrams) method [85]. The Gibbs energy of a particular phase, G, was calculated by using Eq. (14),... 

Polynomial expressions are conveniently used to represent a condensed phase which is stable in the whole temperature range of interest and which does not undergo any structural, electronic or magnetic transformations. The Gibbs energy of a compound is in the CALPHAD approach represented relative to the elements in their defined standard state at 298.15 K as a power series in terms of temperature in the form of [16] ... 

Table 2.2 CALPHAD-type representation of the thermodynamic properties of face-centred cubic (FCC), liquid and hexagonal close-packed (HCP) aluminium of the form (after Dinsdale [18]) ...

N. Saunders and A. P. Miodownik, CALPHAD Calculation of Phase Diagrams a Comprehensive Guide. Oxford Pergamon, Elsevier Science, 1998. 

G. Inden, Proceedings of the Fifth conference on Calculation of Phase Diagrams, CALPHAD V (Dusseldorf) 111(4)1. 

Figure 2.43. Optimization, calculation, prediction of phase diagrams an indication of the working scheme of the CALPHAD method is shown.

It should be remembered that the CALPHAD approach is based on the hypothesis that, for all the phases and structures existing across the complete alloy system, entire Gibbs energy vs. composition curves may be constructed even by extrapolation into regions where they are unstable or metastable. A particular case concerns the pure component elements for which the relative Gibbs energy for the different crystal structures (the so-called lattice stabilities) must also be established and defined as a function of temperature (and pressure). 

The state of the art has been summarized by Colinet (2003) who reported a description of the ab initio calculation methods of energies of formation for intermetallic compounds and a review of the aluminium-based compounds studied. In its conclusions, this paper underlined that the complete ab initio calculation of complex phase diagrams is not close at hand. However, calculation of phase diagrams in systems, where experimental data are missing, could, in the future, be performed by combination of CALPHAD routines and ab initio calculations of formation energies or mixing energies. 

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