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

Abstract

Conceptual role of Short Range phenomenon in Statistical Thermodynamics of liquid alloys is discussed. It is shown why the popular model theories used by Calphad fall short in bringing this phenomenon to full usage. In contrast to this, presented here in details Theory of Inhomogeneous Short Range takes Short Range as basic element of formalism. Combinatorial factor provided by theory expresses the Statistical Sum of entire system as weighed average over Statistical Sums of small groups of atoms conventionally selected in the alloy. Equations of the 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 systems described previously in the literature by Redlich-Kister' polynomials.

Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 3. Association Solution Model Reconstructed

“…Solution to these problems comes from the Theory of Inhomogeneous Short Range Order (TISR) ( [13,17,19]).…”

“…where K ∞ 1 is the high temperature limit of K 1 (that occurs to be equal to N !/(N a !N b ! )); γ is a constant of geometrical nature, that depends on the lattice being considered and on the size of the groups selected for consideration [13]. For example, for the Quasichemical Theory (that is partial case of TISR [19]) γ coincides with the coordination number z of the lattice.…”

“…Detailed description of this subject can be found in [13]. Formally, expression (17) looks just as if the entire energy of system comes from the formation energy of cells.…”

“…and corresponding molar fractions (19) then it occurs that all thermodynamic properties and composition of the system can be expressed through the new reduced variables [13].…”

“…The suggested modifications of ASM bring its basic principles and formalism to a very close similarity with the Theory of Inhomogeneous Short Range Order (TISR) [13]; the few important differences will be discussed.…”