Christopher W. Bale

FactSage Thermochemical Software and Databases

Abstract This paper presents a summary of the FactSage thermochemical software and databases. FactSage was introduced in 2001 and is the fusion of the FACT-Win/F∗A∗C∗T and ChemSage/SOLGASMIX thermochemical packages that were founded over 25 years ago. The FactSage package runs on a PC operating under Microsoft Windows® and consists of a series of information, database, calculation and manipulation modules that enable one to access and manipulate pure substances and solution databases. With the various modules one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. In this article emphasis is placed on the calculation and manipulation of phase diagrams. However the reputation of FactSage has been established mainly in the field of complex chemical equilibria and process simulation where the software has unique capabilities. Some of these capabilities are also shown in this paper.

A modified interaction parameter formalism for non-dilute solutions

A simple modification of the interaction parameter formalism for the thermodynamics of dilute solutions is proposed. The modified formalism reduces exactly to the standard formalism at infinite dilution and preserves the notation as well as the numerical values of the parameters. Hence, existing compilations of interaction parameters can be used directly in the modified formalism. However, the modified formalism is thermodynamically consistent at finite concentrations, whereas the standard formalism is not. Equations for first-order and higher-order modified formalisms are presented for systems of any number of components. In the first-order modified formalism: {fx1211-01}

Mathematical representation of thermodynamic properties in binary systems and solution of Gibbs-Duhem Equation

The storage, retrieval, and manipulation of thermodynamic data with the aid of a computer requires accurate analytical representation of thermodynamic properties of solutions. In the present paper, a critical assessment is made of simple power series expansions and their limitations in representing thermodynamic properties over the entire composition range of a binary system. The advantages of certain orthogonal series as an alternative method of representation is also discussed. Particular emphasis is placed upon series representations which use Legendre polynomials due to their simplicity and the fact that their functional form is consistent with empirical observations of solution behavior. Since the coefficients of orthogonal series are independent of each other when the entire composition range of a binary system is represented, any thermodynamic property can be fitted to any desired degree of accuracy by a finite number of terms without the necessity of storing a large number of significant digits. Also, because the coefficients are uncorrelated, they are amenable to mathematical interpolation and extrapolation as well as to physical interpretation. The relationships between coefficients of series expansions of all partial and integral properties for the general case have been derived using the Gibbs-Duhem equation.

The unified interaction parameter formalism: Thermodynamic consistency and applications

In a recent article, we proposed modifications to the standard interaction parameter formalism. The modified formalism, known as the “Unified Interaction Parameter Formalism,” is discussed in the present article with respect to thermodynamic consistency at finite concentrations in binary, ternary, and multicomponent systems. A new method, which is independent of integration paths, is proposed to derive the equations of the formalism by differentiation of the integral Gibbs energy expression. It is shown that the formalism is thermodynamically exact in both dilute and nondilute composition regions. It is also shown that the formalism reduces to Wagner’s formalism at infinite dilution and to Darken’s quadratic formalism in dilute solutions. Examples are presented and methods are discussed for determining the parameters of the formalism from thermodynamic data.

Simultaneous optimization of thermochemical data for liquid iron alloys containing C, N, Ti, Si, Mn, S, and P

A data base of thermochemical parameters for liquid iron-base alloys containing C, N, Ti, Si, Mn, S, and P is presented. A matrix of linear inequalities describing the experimental data among these elements was constructed. A set of internally consistent thermochemical data permitted by the uncertainties of the experiments was evaluated by means of a linear programming algorithm. Expressions for the interaction parameters of the solutes and the Gibbs energies of formation of the carbides, nitrides, carbonitrides, and sulfides of titanium were simultaneously optimized. It is shown that the resulting thermochemical data base reproduces the experimental data satisfactorily.

Computational techniques for the treatment of thermodynamic data in multicomponent systems and the calculation of phase equilibria

Abstract Various series expansions have been developed which permit experimental data for partial and integral thermodynamic properties of multicomponent phases to be expressed as functions of composition through the use of curve-fitting techniques. These analytical expressions can then be used by the computer to calculate phase equilibria in the system. Examples of the application of the analytical techniques are presented for the systems Zn-Cd-Bi, Cd-Sn-Bi, Fe-Cr-Ni, and S-Cu-Fe. Phase diagrams are calculated for the Zn-Cd-Bi, Cd-Sn-Bi, and Fe-Cr-Ni-O systems. Relationships between the coefficients of series expansions for the partial properties of all the components and the integral properties are developed for series of any number of terms. The relative merits of different types of series expansions are discussed. Techniques are developed for phases with extended ranges of composition, as well as for phases with limited ranges of composition in the vicinity of non-stoichiometric compounds or in solutions rich in one component. In the latter case, the expressions which are developed can be shown to be an extension of “Darkens Quadratic Formalism” to higher-order terms and higher-order systems. A complete discussion of the boundary value problem in the solution of the Gibbs-Duhem equation in multicomponent systems is presented.

Legendre polynomial expansions of thermodynamic properties of binary solutions

The advantages of orthogonal Legendre polynomials for representing the excess thermodynamic properties of binary solutions are presented. It is shown by means of examples that, in searching for empirical correlations among the coefficients of series expansions of several solutions, it is essential to start with a set of coefficients of an orthogonal series. Simple relationships are derived which permit the partial excess properties of each component to be expressed in terms of the same set of Legendre coefficients used for expressing the corresponding integral excess property. The Legendre polynomials are reformulated and the most accurate and convenient means of calculating themvia a simple recursion relationship is described. Explicit conversion formulae from the coefficients of simple power series or Redlich-Kister polynomials to Legendre coefficients are given.

Coupled phase diagram and thermodynamic analysis of the 18 binary systems formed among Li2Co3, K2Co3,Na2Co3, Lioh, Koh, Naoh, Li2So4, K2So4 and Na2So4

Abstract Available phase diagram and thermodynamic data on the eighteen binary systems containing Li+ , Na+, K+, S04=, CO3=, and OH− have been collected and critically assessed. A set of self-consistent thermodynamic parameters describing the free energies of the compounds, solid solutions, and liquid solutions in the binary systems has been formulated. The phase diagrams have been calculated, and estimated error limits of all diagrams are given.

Optimization of binary thermodynamic and phase diagram data

An optimization technique based upon least squares regression is presented to permit the simultaneous analysis of diverse experimental binary thermodynamic and phase diagram data. Coefficients of polynomial expansions for the enthalpy and excess entropy of binary solutions are obtained which can subsequently be used to calculate the thermodynamic properties or the phase diagram. In an interactive computer-assisted analysis employing this technique, one can critically analyze a large number of diverse data in a binary system rapidly, in a manner which is fully self-consistent thermodynamically. Examples of applications to the Bi-Zn, Cd-Pb, PbCl2-KCl, LiCl-FeCl2, and Au-Ni binary systems are given.

Extension to solgasmix for interactive calculations with the F∗A∗C∗7T thermodynamic database

Abstract Professor Erikssons program SOLGASMIX has been combined with user-friendly interactive input and output and with an extensive thermodynamic database and has been made available on-line to North American subscribers to the F∗A∗C∗T (Facility for the Analysis of Chemical Thermodynamics) database. This permits the power of SOLGASMIX to be widely and easily applied to the practical calculation of chemical equilibria. In addition, a subroutine has been written to deal with those cases when SOLGASMIX cannot calculate the equilibrium composition.