H. Okamoto

Thermodynamically improbable phase diagrams

Phase diagrams showing very unlikely boundaries, while not explicitly violating thermodynamic principles or phase rules, are discussed. Phase rule violations in proposed phase diagrams often become apparent when phase boundaries are extrapolated into metastable regions. In addition to phase rule violations, this article considers difficulties regarding an abrupt change of slope of a phase boundary, asymmetric or unusually pointed liquidus boundaries, location of miscibility gaps, and gas/liquid equilibria. Another frequent source of phase diagram errors concerns the initial slopes of liquidus and solidus boundaries in the very dilute regions near the pure elements. Useful and consistent prediction can be made from the application of the van’t Hoff equation for the dilute regions.

guidelines for binary phase diagram assessment

The recent publication of Binary Alloy Phase Diagrams,2nd ed, [90Mas] and our extensive screening of phase diagram graphics for this edition has revealed many phase diagram features, which while not explicitly violating phase diagram rules, are to a lesser or greater extent unlikely to represent thermodynamically acceptable conditions. In two previous papers, several thermodynamically improbable features or boundaries in binary phase diagrams were pointed out [91Oka2], and some unlikely thermodynamic models were shown to be unrealistic, or in error [91Okal]. In the present paper, we discuss some of the unlikely features in more detail in order to develop a set of guidelines that may be useful for checking future proposed phase diagram boundaries, or some specific phase diagram features resulting from both experimental and theoretical work, including also phase diagram assessments.

Binary alloy phase diagrams requiring further studies

Binary Alloy Phase Diagrams , 2nd ed. 90Mas, covering ∼3000 systems and ∼2200 phase diagrams, is the most current compilation of binary systems. However, ∼500 of them include thermodynamically unlikely features. These problems are classified into more than 30 groups, and a few typical examples are shown for each group. If a phase diagram shows an improbable feature, it implies that either the phase diagram is erroneous or a very unique phase diagram situation is occurring in the system. In either case, it is worthwhile to investigate the system in more detail.

Reevaluation of thermodynamic models for phase diagram evaluation

Several thermodynamic models for calculating binary phase diagrams published in the literature have been reevaluated. Problems in some of these models are already evident in the models themselves and may also be seen in the resulting calculated phase diagrams. When a calculation is attempted, thermodynamic models with quite different formulations may result in very similar proposed phase diagrams. In such cases, if experimental data of a binary phase diagram can be represented reasonably well by several different thermodynamic models, a simpler model often provides the clearest insight into the basic properties of the system. If a calculated phase diagram results in unusual phase relationships, the adopted thermodynamic model may be inappropriate or may involve unrealistic parameters. If the thermodynamic model is clearly unrealistic and yet the calculated phase diagram appears to be normal, errors in calculation or in interpretation may be suspect. Various examples of unlikely combinations of thermodynamic models and phase diagrams are discussed.

A two-peak miscibility gap

A possible occurrence of a miscibility gap with two critical points (two peaks) is shown using a subregular solution model. As is well known, an ordinary miscibility gap is developed when elements A and B of the A-B system repel each other, i.e, the enthalpy of mixing is positive. A two-peak miscibility gap is formed when the magnitude of this positive enthalpy of mixing is slightly lowered in the intermediate composition range for some reason, such as a magnetic effect or a tendency toward (imperfectly) forming a compound. The two-peak miscibility gap will lead to a new invariant reaction involving only one type of phase (L2 ↔ L1 + L3, etc). It is likely that two-peak miscibility gaps have never been reported because their existence has not been conceived.

Amorphization process induced by mechanical alloying in the immiscible Cu-Ta system

The mechanism for the amorphization induced by mechanical alloying (MA) has been studied in the immiscible Cu- Ta system. A mixture of copper and tantalum powders at a composition ratio of Ta: Cu = 7:3 was used. The first 30 h of milling essentially results in the reduction in Ta and Cu grain size down to ∼10 nm without measurable formation of an amorphous phase. The thermally assisted amorphization (TAA) becomes noticeable after 60 h of milling. The higher the ambient temperature, the faster the amorphization proceeds. The TAA effect is also observed by annealing a partially amorphous MA powder. The microstructure after 30 h of milling is such that fine Cu crystallites are embedded in a fine- grained Ta matrix. Here an interfacial energy contribution is large enough to raise the Gibbs energy to that of an amorphous phase. Now high temperature milling or annealing allows an energetically downhill process to occur. This is most likely responsible for the observed TAA effect in the Cu- Ta system characterized by a positive heat of mixing.

Errata: The Nb-Si (Niobium-Silicon) system

In Vol. 14, No. 2, p. 273 of “The Magnesium Chloride-Potassium Chloride Phase Diagram,” by G.S. Perry and H. Fletcher, several figures were placed in incorrect figure boxes. Each is an MgC12-KC1 phase diagram. Figure 4 (Ivanov reference) should show the diagram that was placed in the Fig. 5 box. Figure 5 (Chikanov reference) should show the diagram that was placed in the Fig. 7 box. Figure 6 (Grjotheim reference) should show the diagram that was placed in the Fig. 4 box. Figure 7 (Siefert reference) should show the diagram that was placed in the Fig. 6 box. The figures are shown in the correct boxes below.

Effect of ferromagnetism in α-Fe on the form of Au-Fe phase boundaries

Abstract The effect of ferromagnetic interaction in bcc α-Fe on the form of the Au-Fe phase diagram is investigated in this work. An earlier phase diagram modeling indicated that the experimental and calculated (Au)/[(Au) + (α-Fe)] solvus boundaries disagreed significantly. It was speculated that a slow segregation process into (Au) and (α-Fe) caused the disagreement. Present calculation shows that the experimental data correspond to the (Au)/[(Au) + (γ-Fe)] metastable boundary. Therefore, the crystal structure of the initial precipitate in (Au) on cooling may be fcc, the same as that of the matrix.

Thermodynamically Improbable Phase Diagram Features

Interest in phase diagrams, and what they can provide as tools for understanding and solving materials’ problems, has been increasing steadily in all aspects of materials science, stimulated by conferences, book publications, data compilations as well as the numerous phase diagram determinations, evaluations, and calculations published in the literature. In preparing the second edition of evaluated “Binary Phase Diagrams” 1 (published in late 1990 and containing information on nearly 3,000 binary systems), and keeping in mind that the phase diagrams which were about to be published should represent as accurate phase boundary information as possible, we looked at more than 2000 diagrams to be published and continued to discover examples of very unlikely phase boundaries in various respects. Often, the phase diagrams showing problems did not even explicitly violate the well known phase rules. Most of such problems were a challenge to identify, and the majority (but not all) required only a small correction to eliminate. The present article is intended to share some of our observations with the conference participants in the hope that they will stimulate a further discussion of the important connections between phase diagrams and the thermodynamics on which they are based. In two recent publications, several thermodynamically improbable features or boundaries in binary phase diagrams have been pointed out2 and some unlikely thermodynamical models have been shown to be unrealistic, or in error.3 In the present brief paper, we discuss some of the typically unlikely features in order to draw attention to possible guidelines that may be useful for checking future proposed phase diagram boundaries, or some specific phase diagram features resulting from either experimental or theoretical work, including also phase diagram assessments.