Phase diagram CALPHAD methods

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),... 

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

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. 

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... 

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

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. 

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. 

Common approaches for the tailoring of nonmetallic (ceramic) materials properties involve topochemical methods (those where the crystal structure remains largely unaffected) and the preparation of phases in which one or more sublattices are alloyed. In principle, such materials are within the realm of CALPHAD. On the other hand, as has already been stated, extrapolation does not really aid the discovery of new or novel phases, with unique crystal structures. Furthermore, assessed thermochemical data for the vast majority of ceramic systems, particularly transition metal compounds, are presently not available in commercial databases for use with phase diagram software. This does not necessarily preclude the use of the CALPHAD method on these systems However, it does require the user to carry out their own thermodynamic assessments of the (n — 1 )th-order subsystems and to import that data into a database for extrapolation to nth-order systems, which is not a trivial task. 

Through their parallel and independent efforts on both sides of the Atlantic, which began in the 1950s with mathematically modeling known phase diagrams for unary and binary systems, Kaufman and Hillert are considered founding fathers of the CALPHAD method, the field of computational thermodynamics concerned with the extrapolation of phase diagrams for multicomponent systems. (Source L. P. Kaufman, personal communication, February 08, 2004.)... 

The CALPHAD method of computer coupling of phase diagrams and thermodynamics [24] was used to explore the phase equilibria in the Si-B-C-N system. Analytical descriptions of the Gibbs free energies for all stable phases and gaseous species of the system were established in the literature and by the... 

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