There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://dc.engconfintl.org/cgi/viewcontent.cgi?article=1032&context=superalloys_ii

A critical review of high entropy alloys and related concepts

Thermodynamic data for the condensed phases of 78 elements as currently used by SGTE (Scientific Group Thermodata Europe) are tabulated. SGTE is a consortium of seven organisations in Western Europe engaged in the compilation of a comprehensive, self consistent and authoritative thermochemical database for inorganic and metallurgical systems. The data are being published here in the hope that they will become widely adopted within the international community as a sound basis for the critical assessment of thermodynamic data, thereby, perhaps, limiting unnecessary duplication of effort. The data for each phase of each element considered aie presented as expressions showing, as a function of temperature, the variation of (a) G-HSER, the Gibbs energy relative to the enthalpy of the “Standard Element Reference” ie the reference phase for the element at 298.15 K and (b) the difference in Gibbs energy between each phase and this reference phase (ie lattice stability). The variation of the heat capacity of the various phases and the Gibbs energy difference between phases are also shown graphically. For certain elements the thermodynamic data have been assessed as a function of pressure as well as temperature. Where appropriate a temperature— pressure phase diagram is also shown.

Throughout this paper the thermodynamic data are expressed in terms of J mol−1. The temperatures of transition between phases have been assessed to be consistent with the 1990 International Temperature Scale (ITS90).

SGTE data for pure elements

Software for calculation of phase diagrams and thermodynamic properties have been developed since the 1970's. Software and computers have now developed to a level where such calculations can be used as tools for material and process development. In the present paper some of the latest software developments at Thermo-Calc Software are presented together with application examples. It is shown how advanced thermodynamic calculations have become more accessible since: - A more user-friendly windows version of Thermo-Calc, TCW, has been developed. - There is an increasing amount of thermodynamic databases for different materials available. - Thermo-Calc can be accessed from user-written software through several different programming interfaces are available which enables access to the thermodynamic software from a user-written software. Accurate data for thermodynamic properties and phase equilibria can then easily be incorporated into software written in e.g. C++, Matlab and FORTRAN. Thermo-Calc Software also produces DICTRA, a software for simulation of diffusion controlled phase transformations. Using DICTRA it is possible to simulate processes such as homogenization, carburising, microsegregation and coarsening in multicomponent alloys. The different models in the DICTRA software are briefly presented in the present paper together with some application examples.

Thermo-Calc & DICTRA, computational tools for materials science

A description is given of Thermo-Calc, a databank for thermochemistry and metallurgy developed at the division of Physical Metallurgy of the Royal Institute of Technology (KTH) in Stockholm. Using the facilities of Thermo-Calc one can tabulate thermodynamic data, calculate the heat change of chemical reactions and their driving force, evaluate equilibria for chemical systems and phase transformations and calculate various types of multicomponent phase diagrams by an automatic mapping procedure. The databank is quite general and can be applied to all systems where data assessed by a model implemented in the databank are available. The assessment procedure necessary to develop and extend the the databank is discussed. A brief description of the modules of Thermo-Calc is given and two examples are included which demonstrate how flexibly the calculations can be made. These examples will also show that the system is quite easy to use and that there are extensive on-line help facilities.

/pdf/the-thermo-calc-databank-system-2cvjusof17.pdf

The Thermo-Calc databank system☆

On the theory of normal and abnormal grain growth

A mathematical representation of the magnetic specific heat, recently suggested by Inden, was applled to iron in an evaluation of the difference in Gibbs energy between the fcc and bcc states. The resulting equations were then used for a treatment of alloying effects in ferromagnetic metals due to the change of the Curie temperature. The result was approximated in order to conform to the subregular solution model. A strong asymmetric term was obtained.

A model for alloying in ferromagnetic metals

The compound energy formalism

1. Basic concepts of thermodynamics 2. Manipulation of thermodynamic quantities 3. Systems with variable composition 4. Practical handling of multicomponent systems 5. Thermodynamics of processes 6. Stability 7. Applications of molar Gibbs energy diagrams 8. Phase equilibria and potential phase diagrams 9. Molar phase diagrams 10. Projected and mixed phase diagrams 11. Direction of phase boundaries 12. Sharp and gradual phase transformations 13. Transformations in closed systems 14. Partitionless transformations 15. Limit of stability, critical phenomena and interfaces 16. Interfaces 17. Kinetics of transport processes 18. Methods of modelling 19. Modelling of disorder 20. Mathematical modelling of solution phases 21. Solution phases with sublattices 22. Physical solution models.

Phase equilibria, phase diagrams, and phase transformations

Various empirical methods of predicting the properties of a ternary system from its binary components are reviewed and their generalization to higher systems is discussed, The methods are compared by applying the subregular solution model and expressions are derived which allow a direct comparison. For symmetric treatments, a numerical method and equivalent analytical methods are recommended for universal usage. For asymmetric treatments, a numerical method is recommended but the possibility of treating such cases by transforming an asymmetric ternary system into a reciprocal system and using a formally symmetric description is emphasized.

Mats Hillert

Papers

On the theory of normal and abnormal grain growth

A model for alloying in ferromagnetic metals

The compound energy formalism

Phase equilibria, phase diagrams, and phase transformations

Empirical methods of predicting and representing thermodynamic properties of ternary solution phases