Publisher Summary This chapter presents the formalism and applications of cluster expansions to the problem of ab initio calculations of thermodynamic properties of crystalline alloys. The success of the method owes much to the parallel developments of statistical and quantum mechanical methods and, of course, to the availability of powerful computational hardware and software. The technique of orthogonal expansions in cluster functions has revolutionized the treatment of configurationally disordered systems. In addition to offering the most rational and general state-of-order description of alloys, cluster methods provide the rigorous and essential link between quantum and statistical mechanical aspects of first-principles thermodynamic calculations. Cluster functions constitute a complete orthonormal set. This basis set produces a rigorous cluster algebra that is used for systems containing an arbitrary degree of configurational order (or disorder). Cluster methods are, in principle, ideally suited for calculating alloy phase equilibria.

Cluster Approach to Order-Disorder Transformations in Alloys

All available literature on the constitution of Ti−Al is reviewed. Based on a critical evaluation of these data the phase diagram for this system is assessed.

Reassessment of the binary Aluminum-Titanium phase diagram

Modeling concepts for intermetallic titanium aluminides

The Al–B–Nb–Ti system: IV. Experimental study and thermodynamic re-evaluation of the binary Al–Nb and ternary Al–Nb–Ti systems

The Al-B-Nb-Ti system

A thermodynamic description of the Ti-Al system has been developed. Three different analytical descriptions were used to describe the three different types of phases occurring in the Ti-Al system: the stoichiometric compounds, the disordered solution phases, and the ordered inter-metallic compounds which have homogeneity ranges. A least-squares technique was used to optimize the thermodynamic quantities of the analytical description using experimental data available in the literature. The calculated phase diagram, as well as the thermodynamic func-tions, agree well with the critically evaluated experimental data from the literature.

U. R. Kattner

Papers

Thermodynamic Assessment and Calculation of the Ti-Al System