Topology of potential phase diagrams composed of three chemical elements
- PDF / 146,006 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 116 Downloads / 201 Views
Section I: Basic and Applied Research
Topology of Potential Phase Diagrams Composed of Three Chemical Elements Jindrˇich Leitner, Petr Vonˇka, and David Sedmidubský
(Submitted August 15, 2001; in revised form May 11, 2005) A detailed analysis of the topology of two-dimensional isothermal potential phase diagrams for systems composed of three chemical elements is presented. Chemical potentials (or derived properties as activities or partial pressures) of two independent components or their combinations are used as coordinates of such diagrams. The chemical potentials of other species are constant at the given temperature (i.e., stoichiometric, single-species condensed phases, or components of a multicomponent phase of fixed composition). It was shown that only invariant point can change the topology of the diagram. A method for the determination of invariant points is proposed. The set of invariant points is divided into four classes, and each class is demonstrated by a practical example.
1. Introduction Phase diagrams are usually used for the graphic representation of equilibrium phase relations in heterogeneous systems, as a function of intensive variables. The diagrams can often be constructed two-dimensionally. Any pair of intensive variables (e.g., temperature-pressure, temperaturecomposition, pressure-composition, chemical potential [partial pressure]-chemical potential [partial pressure]) can be chosen as coordinates. The diagrams at constant temperature, the coordinates of which are chemical potentials (i) or combinations of chemical potentials (ij ⳱ ␣i − j, where ␣ and  are arbitrary real numbers), or derived variables such as activities (ai) or partial pressures (pi) are called isothermal potential phase diagrams (PPDs) [1998Hil]. As typical examples of PPDs for systems composed of three elements (A-B-C), the Kellogg phase stability diagrams or chemical potential diagrams proposed by Yokokawa and colleagues [1989Yok, 1999Yok] can be given. The former describe the stability of single-species condensed phases in the gaseous atmosphere as a function of log pA and log pB [1981Gas, 1991Pel], whereas the latter use log(aA/aB) and log pc as coordinates. The construction and application of PPDs have been well described in the literature [1986Bal, 1988Rus, 1990Bal, 1990Wan, 1993Lei]. However, the classification and topology of PPDs have almost never been discussed. In this work, we use the definition that two PPDs have different topology if they have either a different number of isothermal invariant points or a different phase composition of some isothermal invariant points. The definition of topology is somewhat ambiguous in the literature. [1990Bal] has studied the topology of intersecting domains in two-metal (i.e., four elements) PPDs and has introduced two different Jindrˇich Leitner, Department of Solid State Engineering, Petr Vonˇka, Department of Physical Chemistry, and David Sedmidubský, Department of Inorganic Chemistry, Prague Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech
Data Loading...
