Calculation of phase diagram

Phase diagrams of geologic interest may be obtained by various method these will be discussed in the following. 

The fundamental basis of this procedure is derived by rearranging eq. ( h) to 

and V being state properties, they are additive as such, lYiK s are also additive. Therefore, if an unknown reaction (x) can be expressed in terms of two (or more) reactions (y) and (z) whose lniC s are known, then In L can be obtained from the relation In/ x y y where Vy and are proper coefficients. 

This method has been immensely popular in geology, one recent example being its application to derive serpentine stability relations (Evans et al.,19T6). 

An analogous procedure is based on the relation AG = - RTlnZ - AV298,s(P-1) 

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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. 

Kaufman, L. and Bernstein, H. (1970) Computer Calculations of Phase Diagrams (Academic Press, New York). 

The example illustrates how Monte Carlo studies of lattice models can deal with questions which reach far beyond the sheer calculation of phase diagrams. The reason why our particular problem could be studied with such success Hes of course in the fact that it touches a rather fundamental aspect of the physics of amphiphilic systems—the interplay between structure and wetting behavior. In fact, the results should be universal and apply to all systems where structured, disordered phases coexist with non-struc-tured phases. It is this universal character of many issues in surfactant physics which makes these systems so attractive for theoretical physicists. 

In conclusion, we have presented a new formulation of the CVM which allows continuous atomic displacement from lattice point and applied the scheme to the calculations of the phase diagrams of binary alloy systems. For treating 3D systems, the memory space can be reduced by storing only point distribution function f(r), but not the pair distribution function g(r,r ). Therefore, continuous CVM scheme can be applicable for the calculations of phase diagrams of 3D alloy systems [6,7], with the use of the standard type of computers. 

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),... 

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. 

The addition of further components makes the presentation of the phase diagrams increasingly complex. The principles are general, however, and calculation of a vertical section in a quinternary system like Fe-Cr-Mo-W-C [19], for example, is fairly easily done by the use of large computer programs for calculation of phase diagrams based on thermodynamics. 

L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams. New York Academic Press, 1970. 

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. 

Saunders, N. and Miodownik, A.R (1998) Calphad Calculation of Phase Diagrams. A Comprehensive Guide, Pergamon Materials Series, ed. Cahn, R.W., (Pergamon, Elsevier Science, Oxford, UK) Vol. 1. 

Curtis, R. A. Blanch, H. W. Prausnitz, J. M. Calculation of Phase Diagrams for Aqueous Protein Solutions. ]. Phys. Chem. B 2001, 105, 2445-2452. 

CALPHAD (Calculation of Phase Diagrams) A Comprehensive Guide... 

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