CALPHAD approach

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] ... 

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). 

One of the objectives of this book is to act as a benchmark for current achievements, but it also has a number of other important general objectives. Despite the undoubted success of the CALPHAD approach, any methodology based on thermodynamic concepts is often erroneously perceived as being difficult to follow, and even considered as unlikely to have a direct practical application because of its association with equilibrium situations. The authors have therefore set themselves the goals of removing such misconceptions and making the book readable by any scientifically competent beginner who wishes to apply or extend the concepts of CALPHAD to new areas. 

The book begins with a chapter describing the history and growth of CALPHAD. This provides a useful point of departure for a more detailed account of the various strands which make up the CALPHAD approach. Chapters 3 and 4 then deal with the basic thermodynamics of phase diagrams and the principles of various experimental techniques. This is because one of basic pillars of the CALPHAD approach is the concept of coupling phase diagram information with all other available thermodynamic properties. It is a key factor in the assessment and characterisation of the lower-order systems on which the properties of the higher-... 

The history of CALPHAD is a chronology of what can he achieved in the field of phase equilibria by combining basic thermodynamic principles with mathematical formulations to describe the various thermodynamic properties of phases. The models and formulations have gone through a series of continuous improvements and, what has become known as the CALPHAD approach, is a good example of what can be seen as a somewhat difficult and academic subject area put into real practice. It is indeed the art of the possible in action and its applications are wide and numerous. 

The roots of the CALPHAD approach lie with van Laar (1908), who applied Gibbs energy concepts to phase equilibria at the turn of the century. However, he did not have the necessary numerical input to convert his algebraic expressions into phase diagrams that referred to real systems. This situation basically remained unchanged for the next 50 years, especially as an alternative more physical approach based on band-structure calculations appeared likely to rationalise many hitherto puzzling features of phase diagrams (Hume-Rotheiy et al. 1940). 

During this period, various aspects of Miedema s methods for predicting the heat of formation of binary compounds were assembled and eventually published in book form (de Boer et al. 1988). This included the application of the technique to predict the thermodynamic behaviour of some ternary compounds. Whilst only applicable to a restricted set of crystallographic structures, this was nevertheless a significant development, as a common objection to the CALPHAD approach was that the existence of ternary compounds could never be predicted solely from binary data. 

Figure 7.16. Comparison of Ni-Al Phase diagrams obtained by (a) using a hybrid CVM-CALPHAD approach (Tso 1992, Cacciamani 1997) and (b) CALPHAD approach incorporating a sub-lattice ordering model (Ansaia et al. 1995).

The aim of this chapter is to introduce the reader to some of the ways in which the CALPHAD approach has been combined with kinetics to predict the formation of phases and/or microstructures under conditions which are not considered to be in equilibrium. Broadly speaking, the combination of thermodynamics and kinetics can be broken down into at least two separate approaches (1) the calculation of metastable equilibria and (2) the direct coupling of thermodynamic and kinetic modelling. 

There are a number of studies where the CALPHAD approach to GFA in amorphous systems has been used. Bormann and co-workers (1988, 1990, 1993) and Saunders and Miodownik (1986) have all used G/x diagrams to help explain the formation of amorphous phases in SSAR. This work has shown that as well as... 

Phase diagrams are calculated from these data using regular solution or other appropriate solution models. Some of the great strengths of the CALPHAD approach are that it provides immediate, approximate diagrams for new systems of interest and that it can be readily extended to ternary and higher order systems that would be prohibitively complex and expensive to study experimentally. A comparison of the... 

Because of its high gravimetric storage capacity LiBH4 has attracted, and still attracts, much attention from various research groups. Nevertheless, the thermodynamic properties are far from ideal for most applications. By use of the CALPHAD approach Cho et al. [86] determined the decomposition temperature of pure LiBH4 at 1 bar Hz pressure to be 403 °C. 

Several authors have also modeled the phase equilibria in the Cr-Fe-Mo system theoretically. [1975Kau] applied the CALPHAD approach to this system. All intermetallic phases were described as stoichiometric. The most detailed theoretical modeling was carried out by [1988And], later augmented by [1992Qiu]. They also used the CALPHAD method. 

In this paper we show how to use a thermodynamic database in a general Calphad approach (3,4) and to understand phases stabilities of diermoelectric materials. Material microstructures after sintering and thermal behavior are checked with the isothennal section at high temperature. Moreover, Gulliver-Scheil simulations (5,6) (infinite diffusion in liquid phase and no diffusion in solid phase) can be used to determine the solid fractions in a solidfication process and the final microstructure. After an example on lead telluride material we will present the features of a general Calphad t proach in thermoelectric antimonides. 

Palumbo, M. Battezzati, L. (2008). Thermodynamics and kinetics of metallic amorphous phases in the framework of the CALPHAD approach. CALPHA, Vol. 32, No. 2, Gune 2008), pp. 295-314, ISSN 0364-5916... 

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