Short Range Order Modeling in Alloys

The Short and Long Range Orders in alloys can be considered based on a new expression for the combinatorial factor. This expression is more convenient and intuitive than the traditionally used form and can be directly applied to reproduce the results of several good known statistical-thermodynamic models that usually are considered completely independent or even inconsistent.The short list includes quasichemical theory, associated solution model, surrounded atom model, cluster site approximation.As result, the formalism and interpretation of these models are significantly clarified, allowing simultaneously to identify and fix several long standing errors that otherwise could be left unnoticed.Multicomponent generalization of listed models is also critically simplified.For the systems experiencing a phase transition, the advanced version of theory provides a mechanism allowing to reproduce the correct critical temperature of conversion and at the same time to increase significantly the precision of thermodynamic functions.

Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 4. Improved Combinatorial Factor

An improved combinatorial factor allows to reproduce the correct critical tem-peratures for the Ising lattices.As result, the accuracy of thermodynamic values calculated near the criticalpoint increases by the factor 2 - 3 for the most important lattice types.It is shown why one-particle (Bragg-Williams) and two-particle (Quasichemical)approximations cannot be adequately applied for description of important nuancesof interatomic interaction.The problem of negative entropy values manifested at low temperatures andtypical for model theories is discussed. It is being argued that this problem has tobe treated as exaggerated.

Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 1. Basic Formalism

Conceptual role of Short Range Order in Statistical Thermodynamics of liquidalloys is discussed. It is shown why the popular model theories used by Calphadfall short in bringing this phenomenon to full usage. In contrast to this, presentedhere in details Theory of Inhomogeneous Short Range Order takes Short RangeOrder as basic element of formalism. Combinatorial factor provided by theoryexpresses the Statistical Sum of entire system as weighted average over StatisticalSums of small groups of atoms conventionally selected in the alloy. Equations ofthe theory are explicitly resolved in a parametric form.The theory in its tetrahedron approximation is applied, as introductory example,for the presentation the thermodynamic data of multiple two-component systemsdescribed previously by other authors using Redlich-Kister’ polynomials.