Miedema's model is a semi-empirical approach for estimating the heat of formation of solid or liquid metal alloys and 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 Natuurkundig Laboratorium.
It may provide or confirm basic enthalpy data needed for the calculation of phase diagrams of metals, via CALPHAD or ab initio quantum chemistry methods.
For a binary system composed by elements A and B, a generic Miedema Formula could be cast as
{\displaystyle \Delta H=f(ElementA,PhiA,nWSA,VA,ElementB.PhiB,nwSB,VB)}
where terms Phi and nwS are explained and reported below.
[3] Miedema introduced his approach in several papers, beginning in 1973 in Philips Technical Review Magazine with "A simple model for alloys".
[4][5] Miedema described his motivation with "Reliable rules for the alloying behaviour of metals have long been sought.
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.
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."
Free web based applications include Entall [6] and Miedema Calculator.
[8][9] The original Algol program[10] was ported to Fortran.
[11] Miedema's approach has been applied to the classification of miscible and immiscible systems of binary alloys.
"[12] 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".
Transition Metal Alloys (1988),[14] The above list of parameters should be considered as a starting point, which could yield such data (results after Fortran program made available by Emre Sururi Tasci[11] M AM5 AM3 AM2 AM MA2 MA3 MA5 AinM AM MinA Sc -6 -9 -12 -17 -16 -13 -9 -39 -11 -53 Ti -10 -15 -20 -25 -22 -18 -12 -62 -17 -74
Zr -13 -20 -27 -37 -34 -28 -19 -85 -25 -118 Nb -9 -14 -18 -23 -21 -17 -11 -57 -16 -70 Mo -1 -2 -2 -3 -3 -2 -1 -7 -2 -9 Tc -2 -3 -4 -5 -4 -3 -2 -11 -3 -13 Ru -3 -4 -5 -7 -6 -5 -3 -17 -5 -20 Rh -3 -5 -6 -8 -7 -5 -4 -20 -5 -23 Pd -2 -4 -5 -6 -6 -4 -3 -16 -4 -19 La 2 3 4 6 7 6 4 14 5 25 Ce 1 2 3 4 4 3 2 8 3 14 Pr 0 1 1 1 1 1 1 2 1 4 Nd 0 1 1 1 1 1 1 2 1 4 Pm -1 -2 -2 -3 -3 -2 -2 -6 -2 -11 Sm -1 -1 -1 -2 -2 -1 -1 -4 -1 -6 EuII 14 22 29 42 44 38 26 91 30 160 EuIII 79 71 63 46 30 23 15 999 47 90 Gd -1 -1 -1 -2 -2 -1 -1 -4 -1 -6 Tb -1 -2 -3 -4 -4 -3 -2 -9 -3 -15 Dy -1 -2 -3 -4 -4 -3 -2 -9 -3 -15 Ho -1 -2 -2 -3 -3 -2 -2 -7 -2 -10 Er -2 -4 -5 -7 -7 -5 -4 -15 -5 -23 Tm -2 -4 -5 -7 -6 -5 -4 -15 -5 -23 YbII 12 18 25 35 36 29 20 77 25 124 YbIII 32 27 23 14 7 5 3 999 16 18 Lu -4 -6 -7 -10 -10 -8 -6 -23 -7 -35 Hf -11 -17 -23 -30 -28 -23 -16 -71 -21 -98 Ta -9 -13 -17 -22 -20 -16 -11 -54 -15 -67
Rb 35 53 70 106 127 116 82 221 83 476 cs 40 58 76 113 151 169 186 219 111 999 Be -8 -12 -15 -16 -12 -9 -6 -44 -9 -31 Mg 9 13 17 23 21 16 11 61 18 78 Ca 12 18 25 36 37 30 21 77 25 128 Sr 16 24 32 47 51 44 31 99 34 190 Ba 17 25 33 49 55 49 35 103 37 212 Zn -2 -3 -4 -5 -4 -3 -2 14 4 14 Cd 5 8 10 14 12 10 7 58 17 77 Hg 8 12 15 21 20 16 11 74 22 106
As -15 -23 -30 -40 -38 -31 -21 -49 -14 -68 Sb -1 -2 -3 -4 -4 -4 -3 33 10 57 Bi 6 9 12 18 19 16 11 80 26 146 improved data may be found in more recent publications;[15] possibly, in the near future, improvement or insisight of these data could be provided by the extended Calphad databases open collections available at NIMS[16] For instance for Fe-X binary phase diagrams, a list of available databases is as presented in this link [1] and more specifically in this table: