Gibbs Energy Modeling of the Cu-S Liquid Phase: Completion of the Thermodynamic Calculation of the Cu-S System

Abstract

A thorough review and critical evaluation of all experimental sulfur potential and phase diagram data available from the literature has been made for optimizing the Gibbs energy of the copper-sulfur liquid phase at 1 bar total pressure. The extended modified quasichemical model serves as a basis for the mathematical expression of the Gibbs energy of binary Cu-S solutions over the complete composition range. A structurally versatile molten phase ranging from highly metallic via sulfur-rich to pure sulfuric is described simultaneously by a single Gibbs energy function. In combination with the recently published Gibbs energies of all Cu-S solid phases, the complete T-x phase diagram as well as for the first time the log(p S2 =bar) À 1=T diagram is calculated. A limited set of obtained model parameters reproduces a large body of data within experimental uncertainties.

The High-Temperature Cu-Fe-S System: Thermodynamic Analysis and Prediction of the Liquid–Solid Phase Range

“…This is the case at around 1/2 mol fraction of sulfur in the Fe-S system [10] and at around 1/3 mol fraction of sulfur in the Cu-S system. [12] Naturally, short-range ordering plays also a dominant role within the ternary Cu-Fe-S liquid solution. As a consequence, a thermodynamic model for the ternary melt over the entire composition range from purely metallic to pure liquid sulfur solutions should be able to merge properly short-range ordering emanating even asymmetrically from both metal-sulfur systems.…”

“…is predicted based on previous optimizations of the binary subsystems Fe-S, [10] Cu-S, [12] and Cu-Fe [13] using the onesublattice modified quasichemical model for multicomponent solutions by Pelton et al [26] and Pelton and Chartrand. [27] Table 1 Excess Gibbs energy parameters (in J mol -1 ) and model quantities of the liquid, bcc, fcc and pyrrhotite phase according to binary optimization studies by Waldner and Pelton, [10] Waldner, [11,12] and Ansara and Janson, [13] The term within the brackets of Eq 1 contains the molar Gibbs energies g o Cu , g o Fe and g o S of the pure components weighted with the numbers of moles of copper, iron and sulfur denoted with n Cu , n Fe and n S . The product of the temperature T and the configurational entropy DS config considers the energetic contribution due to random mixing of the (Cu-Cu), (Fe-Fe), (S-S), (Cu-S), (Fe-S), and (Cu-Fe) pairs in the one-dimensional Ising approximation: [26,27]…”

“…The other coordination numbers in Eq 7 and 8 are defined in the same way when iron and sulfur are the central atoms within their corresponding neighborhood. The assessment of these quantities is treated in detail in the metal-sulfur binary studies [10,12] from which numerical values are taken for this work: A value of 6.0 for the unary coordination numbers Z Cu CuCu , Z Fe FeFe , Z S SS , and the binary coordination numbers Z Cu CuFe and Z Fe CuFe , the values 1.5 and 3.0 for the binary coordination numbers Z Cu CuS and Z S CuS , respectively, and a value of 2.0 for Z Fe FeS and Z S FeS .…”

“…Equation 12 reduces to the excess Gibbs energy of the Cu-S binary system when no iron is present and consequently X CuFe and X FeFe are zero. The adjustable, and in case of necessity temperature dependent parameters Dg o CuS , g io CuS and g oj CuS were optimized in the thermodynamic modeling study of the Cu-S liquid phase [12] . The superscripts noted as a ring, i and j identify the parameters given in the study of Waldner [12] as follows: The parameter Dg o CuS contributes decidedly to the excess Gibbs energy in the composition region where (Cu-S) pairs are dominating.…”

“…The aim of the present study is the prediction of sulfur potentials of the ternary Cu-Fe-S liquid solution applying the modified quasichemical model (MQM) solely on the basis of optimization studies of the binary subsystems Fe-S, [10] Cu-S, [11,12] and Cu-Fe [13] without the use of ternary parameters. Despite different internal structures of the liquid phase ranging from metallic over matte-like to pure liquid sulfur solutions the mathematical description should be cast in one single Gibbs energy expression.…”