HomeAbout this Metal Activity Calculator

Data Sources

The interaction parameters in liquid iron alloys are sourced from Table 2.1, p280-293 in [2] and have been converted to the ${\epsilon }_i^j$ form using Equation (20), p276, in the same text. Any data derived at a temperature other than the reference temperature (1873K) is adjusted to the reference temperature using Equation (17) from [2].

There have been a number of revisions to these values, as listed here:

• ${\epsilon }_{\mathrm{Si}}^{\mathrm{Si}}$ was revised using data from [4].

• ${\epsilon }_{\mathrm{Si}}^{\mathrm{Ni}}$, ${\epsilon }_{\mathrm{Si}}^{\mathrm{Co}}$, ${\epsilon }_{\mathrm{Si}}^V$, ${\epsilon }_{\mathrm{Si}}^{\mathrm{Cr}}$, ${\epsilon }_{\mathrm{Si}}^{\mathrm{Nb}}$, ${\epsilon }_{\mathrm{Si}}^{\mathrm{Mo}}$, ${\epsilon }_{\mathrm{Si}}^W$ were revised using data from [7].

The gamma zero (${\gamma }_i^0$) values for each element in liquid iron are taken from Table 1, p278 in [2] and for convenience the natural logarithm is computed. These values are then adjusted to the reference temperature (1873K) using Equation (16) from [2].

There have been a number of revisions, and additions, to these values, as listed here:

• ${\gamma }_H^0$, ${\gamma }_N^0$, ${\gamma }_O^0$, ${\gamma }_P^0$, ${\gamma }_S^0$, ${\gamma }_{\mathrm{Ga}}^0$, ${\gamma }_{\mathrm{Ge}}^0$, ${\gamma }_{\mathrm{Hf}}^0$, ${\gamma }_{\mathrm{Re}}^0$ were estimated by Wade and Wood.

• ${\gamma }_{\mathrm{Si}}^0$, ${\gamma }_{\mathrm{Ni}}^0$, ${\gamma }_{\mathrm{Co}}^0$, ${\gamma }_W^0$, ${\gamma }_{\mathrm{Mo}}^0$, ${\gamma }_{\mathrm{Cr}}^0$, ${\gamma }_V^0$, ${\gamma }_{\mathrm{Nb}}^0$ were revised using p479 from [7].

Method

The algorithm is implemented in PHP and computed in double precision by the web server at the time that the data file is uploaded. For convenience results are temporarily retained by the server, but it is encouraged that users should download the results as soon as possible.

The algorithm follows these steps:

1. The entire data file is parsed for correctness. If errors are detected then these are reported to the user and the algorithm aborted.
2. From the samples listed in the data file a list of unique temperatures is generated. For each unique temperature a table of interaction parameters (${\epsilon }_i^j$) and gamma zeros (${\gamma }_i^0$) are computed using Equations (17) and (16), respectively, from [2].
3. Then, for each sample composition:
   1. The composition is converted to mole fraction (if required).
   2. The composition is normalised.
   3. The $ln{\gamma }_1$ term is computed using Equation [23] from [3].
   4. For each element (i) the $ln{\gamma }_i$ term is computed using Equation [24] from [3].
   5. If desired, the theoretical saturation of C is computed using the method described on p604 of [5] and the computation is then repeated from (ii.) using this adjusted composition. Convergence is typically achieved in 4 to 5 iterations.
   6. The activity coefficients (${\gamma }_i$) are reported to the user and can be downloaded as a CSV file.

References

[1] Wade, J & Wood, BJ, "Core formation and the oxidation state of the Earth", EARTH AND PLANETARY SCIENCE LETTERS, DOI:10.1016/j.epsl.2005.05.017, 2005 [DOI Lookup]

[2] Gordon and Breach, "Steelmaking Data Sourcebook", Gordon and Breach Science Publishers, ISBN:2-88124-153-0, 1988 [ISBN Lookup]

[3] MA, Zhongting, "Thermodynamic description for concentrated metallic solutions using interaction parameters", Metallurgical and Materials Transactions B, DOI:10.1007/s11663-001-0011-0, 2001 [DOI Lookup]

[4] Bouchard and Bale, "Simultaneous optimization of thermochemical data for liquid iron alloys containing C, N, Ti, Si, Mn, S, and P", Metallurgical and Materials Transactions B, DOI:10.1007/BF02653863, 1995 [DOI Lookup]

[5] Wood, BJ, "Carbon in the core", Earth and Planetary Science Letters, DOI:10.1016/0012-821X(93)90105-I, 1993 [DOI Lookup]

[6] Malhotra, Chang, Schlesinger, "Liquid solution thermodynamics in the alumina-saturated Fe-C-Pb system", ISIJ INTERNATIONAL, DOI:10.2355/isijinternational.38.1, 1998 [DOI Lookup]

[7] Tuff, J, Wood, BJ, Wade, J, "The effect of Si on metal-silicate partitioning of siderophile elements and implications for the conditions of core formation", GEOCHIMICA ET COSMOCHIMICA, DOI:10.1016/j.gca.2010.10.027, 2011 [DOI Lookup]