Miedema's model

Miedema's model is a semi-empirical approach for estimating the heat of formation of solid or liquid metal alloys and /or compounds in the framework of thermodynamic calculations for metals and minerals.^[1] It was developed by the Dutch scientist Andries Rinse Miedema ( 15 November 1933 - 28 May 1992 ^[2] ) while working at Philips Research Laboratories Philips_Natuurkundig_Laboratorium. It may provide or confirm basic enthalpy data that have always been needed for the calculation of phase diagrams of metals, and that are now currently approached by CALPHAD. The method has been introduced by Miedema in a couple of papers appeared in 1973 in Philips Technical Review Magazine entitled "A simple model for alloys".^[3][4] While Miedema himself or with collaborators produced many scientific papers we report here in his own words the genuine motivation of his approach "Reliable rules for the alloying behaviour of metals have long been sought. There is the qualitative rule that states that the greater the difference in the electronegativity of two metals, the greater the heat of formation - and hence the stability. Then there is the Hume-Rothery rule, which states that two metals that differ by more than 15% in their atomic radius will not form substitutional solid solutions. This rule can only be used reliably (90 % success) to predict poor solubility; it cannot predict good solubility. The author has proposed a simple atomic model, which is empirical like the other two rules, but nevertheless has a clear physical basis and predicts the alloying behaviour of transition metals accurately in 98 % of cases. The model is very suitable for graphical presentation of the data and is therefore easy to use in practice." There are several free web bases applications like Entall ^[5] or Miedema Calculator.^[6] The latter has been recently reviewed and improved, with an extension of the method in a scientific publication.^[7] A simple presentation of the method is in the appendix B of the book,^[8] while the original Algol program ^[9] has been ported in a fortran code ^[10]

Implication of Miedema's model on an informatics guided classification of miscible and immiscible binary alloy systems

A recent open journal work ^[11] emphasizes the capabilities of Miedema's approach in the classification of miscible and immiscible systems of binary alloys. These are extremely relevant in the design of multicomponent alloys. The paper by mining data from hundreds of experimental phase diagrams, and thousands of thermodynamic data sets from experiments and high-throughput first-principles (HTFP) calculations, obtains a comprehensive classification of alloying behavior for 813 binary alloy systems consisting of transition and lanthanide metals. "Impressively, the classification by the miscibility map yields a robust validation on the capability of the well-known Miedema’s theory (95% agreement) and shows good agreement with the HTFP method (90% agreement). These 2017 results demonstrate that "a state-of-the art physics-guided data mining can provide an efficient pathway for knowledge discovery in the next generation of materials design". See also the html version of the paper by Zhang, R.F., Kong, X.F., Wang, H.T., Zhang, S.H., Legut, D., Sheng, S.H., Srinivasan, S., Rajan, K., Germann, T.C.

References

See also

• Phase diagram
• Gibbs energy
• CALPHAD
• Intermetallic compound
• Enthalpy of mixing
• Computational thermodynamics