CALPHAD methods

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

Chapter S examines various models used to describe solution and compmmd phases, including those based on random substitution, the sub-lattice model, stoichiometric and non-stoichiometric compounds and models applicable to ionic liquids and aqueous solutions. Tbermodynamic models are a central issue to CALPHAD, but it should be emphasised that their success depends on the input of suitable coefficients which are usually derived empirically. An important question is, therefore, how far it is possible to eliminate the empirical element of phase diagram calculations by substituting a treatment based on first principles, using only wave-mecbanics and atomic properties. This becomes especially important when there is an absence of experimental data, which is frequently the case for the metastable phases that have also to be considered within the framework of CALPHAD methods. 

The use of an ideal-solution model meant that there were a number of instances where calculated and experimental results were quantitatively at variance. However, the approach very successfully predicted the general form of most of the phase diagrams, for example whether they were peritectic or eutectic, and accounted for the appearance of intermediate phases in systems such as Cr-Rh. That the approach could do this using such simple and internally self-consistent models is a demonstration of the inherent power of CALPHAD methods. The importance of this first step therefore cannot be overestimated, although its significance was not... 

In many cases the CALPHAD method is applied to systems where there is solubility between the various components which make up the system, whether it is in the solid, liquid or gaseous state. Such a system is called a solution, and the separate elements (i.e., Al, Fe...) and/or molecules (i.e., NaCl, CuS...) which make up the solution are defined as the components. The model description of solutions (or solution phases) is absolutely fundamental to the CALPHAD process and is dealt with in more detail in chapter S. The present chapter will discuss concepts such as ideal mixing energies, excess Gibbs energies, activities, etc. 

Thermodynamic modelling of solution phases lies at the core of the CALPHAD method. Only rarely do calculations involve purely stoichiometric compounds. The calculation of a complex system which may have literally 100 different stoichiometric substances usually has a phase such as the gas which is a mixture of many components, and in a complex metallic system with 10 or 11 alloying elements it is not unusual for all of the phases to involve solubility of the various elements. Solution phases will be defined here as any phase in which there is solubility of more than one component and within this chapter are broken down to four types (1) random substitutional, (2) sublattice, (3) ionic and (4) aqueous. Others types of solution phase, such as exist in polymers or complex organic systems, can also be modelled, but these four represent the major types which are currently available in CALPHAD software programmes. 

Most of this book concerns the development and application of theoretical thermodynamic models, as these are the basis of the CALPHAD method. However, none of this would be possible without the existence of the computational methods and software which allow these models to be applied in practice. In essence, the issues involved in computational methods are less diverse and mainly revolve around Gibbs energy minimisation. In addition, there are optimiser codes which are used for the thermodynamic assessment of phase equilibria. The essential aim of these codes is to reduce the statistical error between calculated phase equilibria, thermodynamic properties and the equivalent experimentally measured quantities. 

CALPHAD methods attempt to provide a true equilibrium calculation by considering the Gibbs energy of all phases and minimising the total Gibbs energy of the system (G). In this circumstance G can be calculated either from knowledge of the chemical potential (Gi) of component i, by... 

Broadly speaking, the first application of CALPHAD methods was intrinsically coupled to experimental thermodynamic or phase-diagram measurements. For... 

The main areas of application for more generalised models have, until recently, been restricted to binary and ternary systems or limited to ideal industrial materials where only major elements were included. The key to general application of CALPHAD methods in multi-component systems is the development of sound, validated thermodynamic databases which can be accessed by the computing software and, until recently, there has been a dearth of such databases. 

J The effect of radiation on the prec itathn of silicides in Ni alloys. While chemical reactions in nuclear generators have dominated how CALPHAD methods have been used in practice for nuclear applications, there has also been a significant interest in the metallurgical aspects of materials under irradiation (Kaufman et al. 

This chapter has shown many examples of the use of CALPHAD methods, ranging from an unusual application in a binary system, through complex equilibrium calculations to calculations for 10-component alloy systems. In all cases the use of CALPHAD methods has enhanced the understanding of processes, clearly defined alloy behaviour and provided vital information for other models, etc. It is also clear that equilibrium calculations can be used in many different areas and under a surprising number of different conditions. For numerous reasons, modelling will never completely replace experimental measurement. However, die quantitative verification of the accuracy of CALPHAD calculations now means that they can be seriously considered as an information source which can be used as an alternative to experimental measurement in a number of areas and can also enhance interpretation of experimental results. 

For a number of applications, particularly those associated with conditions of continuous cooling or heating, equilibrium is clearly never approached and calculations must be modified to take kinetic factors into account. For example, solidification rarely occurs via equilibrium, amorphous phases are formed by a variety of non-equilibrium processing routes and in solid-state transformations in low-alloy steels much work is done to understand time-temperature-transformation diagrams which are non-equilibrium in nature. The next chapter shows how CALPHAD methods can be extended to such cases. 

The forthcoming years will offer a great deal of excitement if the CALPHAD method is extended and infused with new ideas and directions. For our part, we would like to see efforts continue which place CALPHAD on the soundest possible physical basis so that the semi-empirical nature of the subject area can be reduced. This, alongside the exciting new areas of application which are continually appearing, promises to provide the necessary scientific stimulus to keep alive the long pioneering tradition of the early workers in this field. 

Here, we only present the simplest thermodynamic expressions used in the CALPHAD method for the major phase classes observed in multicomponent systems namely, disordered miscible and immiscible phases and ordered sublattice phases. The reader is referred to specialized textbooks for further discussion. The Gibbs energies for disordered two-component solid and liquid solution phases are most easily represented by the regular solution model (Eq. 2.10) or one of its variants ... 

It is possible in many cases to predict highly accurate phase equihbria in multi-component systems by extrapolation. Experience has shown extrapolation of assessed (n — 1) data into an nth order system works well for n < 4, at least with metallurgical systems. Thus, the assessment of unary and binary systems is especially critical in the CALPHAD method. A thermodynamic assessment involves the optimization of aU the parameters in the thermodynamic description of a system, so that it reproduces the most accurate experimental phase diagram available. Even with experimental determinations of phase diagrams, one has to sample compositions at sufficiently small intervals to ensure accurate reflection of the phase boundaries. 

Databases with assessed thermodynamic data for hundreds of substances are available, including alloys, semiconductors, geochemical compounds (silicates and other main-group oxides), aqueous solutions, and molten salts. The bulk of the commercially available databases are on metallurgical systems since the CALPHAD method finds ready applicability in the fields of metals processing and alloy development. 

---