Hello all,
I am looking for a formula or a chart that allows to calculate the resistivity (or conductivity) of a ternary Al Fe Si alloy.
The element content varies a lot, Fe 50%, Al 36 %, Si 11 % for example.
I have found so far only equations for a very small amount of Fe in Al.
Any suggestions where to find it? Thank you.
I am not sure that such a chart may exist in solid state. We made such calculations in the liquid state (Saadeddine et al.) since liquid state is disordered and that we can take into account homo and heterocoordination. More Recently Grosdidier wrote a program for quinary alloys.
In solid state all is more difficult since in general solid alloys are not miscible in all compositions. So an interpolation scheme is only valid, to my opinion, in specific situations like substitutional alloys. The calculation of the resistivity of alloys is possible for liquid state because the structure factors have broad peaks. The value of 2 kF moves (by changing composition) in smooth structure factor hills, so the resistivity is in general a convex curve with composition. In solid state the hills transform in sharp peaks especially at low temperature.
More in solid state we have a polycrystal more or less homogeneous; the size of the grains can change, grain boundaries have more or less importance, many defects exist, the polycrystal can be textured and the composition of the grain can be different for ternaries and above and so on. The resistivity may change abruptly when 2kF moves from the left to the right of the (sharp) first peak structure factor.
I think interpreting the resistivity of solid state can be done, difficultly and only in very specific situations.
In the following, the alloy shall be taken as a compact material, with null porosity. Let us tentatively accept that the following correlation reasonably predicts (estimates) the density of the alloy (ρ): 1/ρ ≈ g1·w1/ρ1 +... + gi·wi/ρi +... + gn·wn·/ρn, where gi are empirical fitting coefficients to be fitted from the available experimental data, while wi is the mass fraction of a generic component (∑wi = 1). If no such data is available, we may want to take all these coefficients as the unit (gi = 1), so that we would be dealing with a ‘mixture rule’ to estimate the density of the alloy, rather than with a correlation. The alloy components here considered are not necessarily the elements, as they may include intermetallic phases (e.g. Al3Fe), possibly taken from the vertex of a pseudo-ternary diagram used to represent the alloy compositions of interest. The electrical conductivity (σ) has SI units of siemens per meter (S/m); so that those of its cube, σ3 are (S3/m3), being, therefore, comparable to those of density (kg/m3). The following correlation now seems dimensionally appealing: 1/σ ≈ [f1·w1/σ13 +... + fi·wi/σi3 +... + fn·wn·/σn3]1/3, where fi are empirical fitting coefficients, while σi stand for the electrical conductivity of the considered components. Again, in the absence of experimental data available, we may want to take all fi = 1, what leads us to a ‘mixture rule’, which hopefully, may be able to (roughly) estimate the electrical conductivity of the alloy for a given composition. It is important to notice, however, that the conductivity largely depends on microstructural features of the alloy that were not properly accounted for, by such a compositional-based empirical approach, which is also deprived of thermodynamic support.
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