Miedema’s model

Miedema s model and parameters and prediction of compound formation capability. A semi-empirical approach to the evaluation of the compound formation capability and of the heats of formation of alloys was proposed by Miedema and co-workers. This resulted in a model which became very popular and, especially because there was scarcity of experimental data, was frequently used in the evaluation, even if approximate and several times incorrect, of the formation enthalpies. The model suggested for energy effects in alloys is well known essentially it is based on the definition of two parameters. By assigning two coordinates... 

Some aspects of the mentioned relationships have been presented in previous chapters while discussing special characteristics of the alloying behaviour. The reader is especially directed to Chapter 2 for the role played by some factors in the definition of phase equilibria aspects, such as compound formation capability, solid solution formation and their relationships with the Mendeleev Number and Pettifor and Villars maps. Stability and enthalpy of formation of alloys and Miedema s model and parameters have also been briefly commented on. In Chapter 3, mainly dedicated to the structural characteristics of the intermetallic phases, a number of comments have been reported about the effects of different factors, such as geometrical factor, atomic dimension factor, etc. on these characteristics. 

Table G. 1 reproduces values calculated by Miedema s model (Niessen et al. 1983) for the partial enthalpy of solution at infinite dilution of a liquid metal solute i in a liquid metal solvent i, AH, (in kJ/mole). For a i-j alloy, the regular solution parameter k can be approximated by [AHj(j( + AHJ(l)]/2.

We will briefly discuss here the two principal semi-empirical models Miedema s model and the semi-empirical band structure model. 

In general, the plateau pressure of reaction (4.18) will also be much higher than in reaction (4.15). For example, the dissociation pressure of ZrNiH2 is 10 higher than for ZrH2 [46]. In Miedema s model, it is assumed that, in a compound, the atomic cells of metals A and B are similar to the atomic cells of the pure A and B metals. A schematic representation of the unit cell is given in Figure 4.4. 

Where, from fitting experimental values, the parameters a and p are determined to be equal to 29.62 kj eV (molH) and —135 kj (molH) , respectively [71, 72]. This model could also be applied to ternary hydrides with an agreement with experimental values that is generally better than Miedema s model. Figure 4.5 shows a comparison between experimental and calculated heats of formation for various ternary... 

Fig. 3.26. Maximum negative enthalpies of mixing Affm in Co5STM45 alloys calculated by Miedema s model [3.59] and observed glass-forming ranges AGFR [3.57]...

Phase stabiUties of metastable solid solutions (amorphous, bcc, hep) and stable Zr(Fe,Cr)2 phase have been calculated by [2002Rod] using Miedema s model in order to explain alloy amorphization and Fe depletion of the Zr(Fe,Cr)2 precipitates in Zircaloy irradiated at intermediate temperatures. 

Crystallization temperature (T ) for several amorphous alloys and formation enthalpies (AH) calculated by means of Miedema s model for the corresponding (hypothetical) intermetallic compounds. The AH values are given in units of kj per mol of alloy (Miedema et al., 1980). 

The second term represents the analog of the repulsive term in the heat of formation in Miedema s model (Miedema et al., 1980). The sign of the coefficient Q follows from the contention that the mismatch in electron density at the Wigner-Seitz atomic cell boundaries (/i,, ) in transition metal alloys can be removed by means of s-d intra-atomic electron conversion. The s electrons reside predominantly in the outside regions of the atomic cell. Conversion of s-type electrons into d-type electrons will therefore result in a decrease of n. It follows then that P and Q are of opposite sign. 

Ray PK, Akinc M, Kramer MJ (2010) Applications of an extended Miedema s model for ternary alloys. J Alloys Comp 489 357-361... 

Calculation of the GFA of alloys based on Miedema s model 2.2.1 Method... 

Miedema s model is an empirical theory for calculating heat of mixing in various binary systems both for the solid state (Miedema et al., 1975) and liquid (Boom et al., 1976). This model involves the calculations of the formation enthalpy of metallic glasses (amorphous... 

Fig. 3. Hypothetical Gibb s free energy diagram for a) "pure" Zr Rh and b) Zr, Rh H. Note that the quantitative differences of the free energies for tJie phases are arbitrarily chosen but there is qualitative agreement with prelimary calculations using Miedema s model.

Kleppa and his coworkers measured the enthalpies of formation of a series of intermetallic compounds between rare earth metals and transition metals by accurate high temperature calorimetric method [62]. Based on these data, we have used SVR-based feature selection method (this method is described in Chapter 4 of this book) to search the optimal set of atomic parameters for support vector regression. It has been found that an effective feature set suitable for the computerized prediction of the enthalpy of formation of these compounds includes only two parameters Miedema s A< ) and the ratio of atomic radii R1/R2 (here the values of the atomic radius proposed by Teatum are used). By SVR and leave-one-out (LOO) cross-validation, the results of prediction are rather good. Table 7.1 shows the comparison between the experimental values and the predicted values of the enthalpy of formation of these compounds. The results of calculation by Miedema s model [104] are also listed for comparison. 

In Miedema s model the heat of formation AH of an intermetallic compound. Ri M comprises two contributions ... 

Semi-empirical values of and are listed for all common metals, so that AH can be calculated for almost all metal combinations (Miedema et al., 1980). Values of AH calculated on the basis of Miedema s model for a representative number of compounds are reproduced in table 2. 

Miedema s model is able to give quite a reliable answer to the question of whether... 

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