Gibbs energy minimisation

Chapter 9 deals with the general principles of computational thermodynamics, which includes a discussion of how Gibbs energy minimisation can be practically achieved and various ways of presenting the output. Optimisation and, in particular, optimiser codes, such as the Lukas progranune and PARROT, are discussed. The essential aim of these codes is to reduce the statistical error between calculated phase equilibria, thermodynamic properties and the equivalent experimentally measured quantities. 

One method would be to use Eq. (3.62) and utilise a Newton-Raphson technique to perform a Gibbs energy minimisation with respect to the composition of either A or B. This has an advantage in that only the integral function need be calculated and it is therefore mathematically simpler. The other is to minimise the difference in potential of A and B in the two phases using the relationships... 

Figure 9.7. Schematic diagram showing first iteration stage in the Gibbs energy minimisation process of an alloy with composition zo in Ni-Cu at 1523 K.

Figure 9.14. Schematic diagram showing Gibbs energy minimisation process for an alloy of composition zq in Ni-Cu at 1523 K incluthng a metastable phase 0.

One of the earliest examples of Gibbs energy minimisation applied to a multi-component system was by White et al. (1958) who considered the chemical equilibrium in an ideal gas mixture of O, H and N with the species H, H2, HjO, N, N2, NH, NO, O, O2 and OH being present. The problem here is to find the most stable mixture of species. The Gibbs energy of the mixture was defined using Eq. (9.1) and defining the chemical potential of species i as... 

The equilibrium calculations in ChemApp are performed by the same Gibbs energy minimisation code as in the well-known interactive software ChemSage, now FactSage, and are thus of proven reliability. 

Kulik, D. A. (2002a). Sorption modelling by Gibbs energy minimisation towards a uniform thermodynamic database for surface complexes of radionuclides. Radiochim. Acta 90, 815-832. 

The computer program SOLGASMIX [4] calculates the equilibria according to the principle of Gibbs energy minimisation at a constant pressure and temperature. 

The available thermodynamic data are of two types stabihty constants, enthalpy and entropy of reaction for the formation of soluble complexes Th(S04) " " and solubihty data for various solid phases. The two sources are linked because the solubility of the solid phases depends on the chemical speciation, i.e., the sulphate complexes present in the aqueous phase. The analysis of the experimental stability constants has been made using the SIT model however, this method cannot be used to describe the often very high solubility of the solid sulphate phases. In order to describe these data the present review has selected a set of equilibrium constants for the formation of Th(S04) and Th(S04)2(aq) at zero ionic strength based on the SIT model and then used these as constants in a Gibbs energy minimisation code (NONLINT-SIT) for modelling experimental data to determine equilibrium constants for the formation of Th(S04)3 and the solubility products of different thorium sulphate solids phases. 

The Gibbs energy minimisation and optimisation program, NONLINT-SIT... 

In this Appendix, no attempt will be made to present details of all the equations involved in calcnlations we restrict onrselves to a very general description of the for-mnlation of Gibbs-energy minimisation problem and the optimisation procedure, illustrated by an example. Readers interested in the details of the programs and the detailed equations involved shonld consnlt [1995FEL] and the very detailed nser mannal of INSIGHT, [1997STE/FEL]. 

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