The CaO–Al2O3–SiO2 system has been assessed with the CALPHAD technique, based on recent assessments of its binary systems. A new species AlO2−1 was introduced for modeling liquid Al2O3. The ternary ...liquid phase was described using the ionic two‐sublattice model as
. The available experimental data were critically examined, and a self‐consistent set of thermodynamic descriptions was obtained. Various phase diagrams and property diagrams, including isothermal sections, isoactivity lines, and a projection of the liquidus surface, are presented. Information on viscosity seems to support the use of the AlO2−1 species.
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The compound energy formalism Hillert, Mats
Journal of alloys and compounds,
05/2001, Volume:
320, Issue:
2
Journal Article
Peer reviewed
The compound energy formalism for solution phases with sublattices is very flexible and thermodynamic models for a large variety of phases have been constructed within this formalism. The range of ...applications is reviewed and the methods of handling various problems are examined. Recent developments including treatments of short range order within the compound energy formalism are reviewed.
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Computational tools allow material scientists to model and analyze increasingly complicated systems to appreciate material behavior. Accurate use and interpretation however, requires a strong ...understanding of the thermodynamic principles that underpin phase equilibrium, transformation and state. This fully revised and updated edition covers the fundamentals of thermodynamics, with a view to modern computer applications. The theoretical basis of chemical equilibria and chemical changes is covered with an emphasis on the properties of phase diagrams. Starting with the basic principles, discussion moves to systems involving multiple phases. New chapters cover irreversible thermodynamics, extremum principles, and the thermodynamics of surfaces and interfaces. Theoretical descriptions of equilibrium conditions, the state of systems at equilibrium and the changes as equilibrium is reached, are all demonstrated graphically. With illustrative examples - many computer calculated - and worked examples, this textbook is an valuable resource for advanced undergraduates and graduate students in materials science and engineering.
Isothermal information is rarely available for the formation of martensite in Fe or Fe alloys due to a very high rate of transformation compared to the rate of heat conduction. Such information has ...now been extracted for lath martensite in some sets of Fe alloys from available information on ultra-rapid quenching but only at a single temperature for each alloy, related to its two M
S
temperatures. The temperature dependence could, thus, be studied only on binary sets of alloys. Those results have been applied to mathematical models based on the Arrhenius equation and illustrated with Arrhenius plots. For three sets of binary Fe alloys, a large group of rates came close to the rate of an almost pure and carbon-free Fe-C alloy. It illustrated that Cr, Ni, and Ru in low contents have relatively small effects on the rate of formation of lath martensite in Fe. It also demonstrated that the present measurements have considerable reproducibility. In contrast, a set of Fe-C alloys did not give a straight line in the Arrhenius plot. Using a new mathematical model based on the concept of the Arrhenius equation to express the effect of carbon, it was possible to predict the rate of formation of lath martensite for Fe-C alloys with fixed C content and their temperature dependencies which are not available experimentally due to the very high rate of formation.
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Information on the diffusional transformation products of austenite in high-carbon steels is reviewed and supplemented with new microscopic studies. A comparison with transformation products in ...low-carbon steels indicates that there is a symmetry with pearlite in the middle, where ferrite and cementite are equal partners, and with acicular ferrite or cementite on each side. They both form with a surface relief, and at lower temperatures, each one is the leading phase in a eutectoid microstructure, bainite and inverse bainite, respectively. However, there is an asymmetry because at low temperatures bainite appears in high-carbon steels but inverse bainite never appears in low-carbon steels. At a constant high carbon content, there is another kind of symmetry, which is related to temperature. At intermediate temperatures the eutectoid reaction results in spherical nodules in which the cementite constituent originates from Widmanstätten plates. It turns spiky at both higher and lower temperatures with the leading phase in the spikes being cementite at higher temperatures and ferrite at lower temperatures. In the first kind of symmetry, there is an abrupt change among the three reaction products; in the second kind of symmetry, there is a gradual change. Accepting that all the eutectoid microstructures form by diffusion of carbon, one may explain the existence of both symmetries by the variation of the ratio of the supersaturations of ferrite and cementite with carbon content and with temperature.
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The role of vacancies in thermodynamic models based on the compound energy formalism, CEF, is studied by application to a binary phase with two sublattices where the two components occupy one ...sublattice each. Vacancies were introduced in CEF by considering them as a chemical component. It is argued that this is not correct and their content is rather an internal variable. The variation in constitution is illustrated with a square-shaped diagram with corners representing the end-members. On two sides, the model degenerates to substitutional models of vacancies in either component. They meet in a corner representing only vacancies. For consistency, it may seem that all three models should represent the same physical state in that corner which is not true. The conflict was resolved by studying the molar Gibbs energy expressions of the models. The problem with multiple solutions is analyzed in terms of a critical state where the first, second and third derivative of the molar Gibbs energy vanish.
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There are two popular methods for storing Gibbs energy data for pure substances. They are inspired by Planck and by Lewis and Randall and may appear as very different but it will be demonstrated that ...they only differ by the choice of references. The derivation of functions to be stored will then be described and a crude but very simple method for extending them to 0K by interpolation instead of extrapolation will be presented.
•Lattice stability procedure for Gibbs energy of metastable allotropes is modified.•Nernst's heat theorem for 0K is satisfied.•Effects on Gibbs energy and derived quantities are demonstrated with calculations.•The method can also be applied to stoichiometric compounds.
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18.
Morphology of Upper and Lower Bainite with 0.7 Mass Pct C Yin, Jiaqing; Hillert, Mats; Borgenstam, Annika
Metallurgical and materials transactions. A, Physical metallurgy and materials science,
09/2017, Volume:
48, Issue:
9
Journal Article
Peer reviewed
Open access
There has been an on-going discussion on the difference in formation mechanisms of upper and lower bainite. Various suggestions have been supported by reference to observed morphologies and ...illustrated with idealized sketches of morphologies. In order to obtain a better basis for discussions about the difference in mechanism, the morphology of bainite in an Fe-C alloy with 0.7 mass pct carbon was now studied in some detail from 823 K to 548 K (550 °C to 275 °C) at temperature intervals of 50 K or less. The work focused on bainite seen to start from a grain boundary in the plane of polish and showing an advancing tip in the remaining austenite. The results indicate that there is no essential difference with temperature regarding the ferritic skeleton of feathery bainite. The second stage of bainite formation, which involves the formation of both ferrite and cementite, was regarded as a eutectoid transformation and the resulting morphologies were analyzed in terms of two modes, degenerate and cooperative eutectoid transformation. There was no sharp difference between upper and lower bainite. Ways to define the difference were discussed.
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There are several phenomena that depend on the interaction between solute atoms and migrating grain boundaries or phase interfaces. In order to explain them several models have been proposed and ...these are now reviewed. There are two approaches to this problem: the solute drag approach and the Gibbs energy dissipation approach. The latter has often been applied to a sharp interface model resulting in a treatment that is in accord with expectations from irreversible thermodynamics. When applied to the homogeneous interface model there are problems at high velocities. When applied to a wedge-shaped description of the properties of the interface, a very flexible treatment is obtained but it is difficult to decide how to choose the model parameters. The application of the solute drag approach to phase transformations is discussed. It is postulated that it should give the same result as the dissipation approach and this can be proved in simple cases. Applications to massive transformation, the effect of alloying elements on the formation of ferrite from austenite and DIGM are discussed.
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The thermodynamic modelling of solid (crystalline) phases forms a central topic within the
Calphad approach and a variety of aspects have been discussed at previous Ringberg workshops. At the present ...Ringberg workshop, modelling of volume and its temperature, pressure and composition dependence formed a major part of the discussions. In addition, modelling of the heat capacity above the (equilibrium) melting temperature, sublattice modelling of complex phases, modelling of ordering and interstitial solutions in the bcc lattice and the effect of magnetism were addressed.
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