### 2.2.2 Alloys

| Pure metals are rarely used - in the real world you use alloys.
|  | In principle, the specific resistivity r of an alloy can be obtained from the phase diagram and the r - values of the phases involved. Lets look at the extremes:
| 1. Complete immiscibility, e.g. in the case of Au/Si, or Cu/W. We may treat the resulting mix of metal particles as a network of resistors being linked in series and parallel. The volume fractions of the phases would constitute the weights - the treatment is not unlike the elastic modulus of compounds.
|  | But no matter what kind of volume fraction you use and how you treat the resistor network - the resulting resistivity will never be smaller than that of the ingredient with the smallest resistivity.
| 2. Complete miscibility (e.g. Au/Ag, Cu/Ni). Experimentally we find for small amounts (some %) of B in A (with [B] = concentration of B)
r » rA + const. · [B]
|  | This formula is a special case of Nordheims rule which states .
r » XA · rA + XB · rB + const. · XA ·XB
|  | This is pretty much an empirical law, it does not pay to justify it theoretically. Again, it is not possible to produce an alloy with a resistivity smaller than one of its components.
| If you have intermetallic compounds in your phase diagram, use Nordheim's rule with the intermetallic phases as XA and XB.
|  | This leaves open the possibility that some intermetallic phase, i.e. a defined compound with its own crystal lattice, might have a lower resistivity than its constituents. While this is unlikely (if not outright impossible?) on theoretical grounds, no such intermetallics have been found so far.
| The sad fact then is that unleashing the full power of metallurgy and chemistry on mixing conductors (i.e. metals), will not give you a conductor with a specific conductivity better than Ag.
|  | You will have to turn to superconductors (forgetting about cost considerations), if you can't live with Ag.

| Lets look at some examples:
| Complete miscibility (e.g. Au/Ag) | Miscibility gap (e.g. Ag/Cu); phase diagram in the link. | Intermetallic phases (e.g. Cu/Au)

| What do we learn? Something simple:
|  | Again: The resistivity always goes up in alloys or mixed materials as compared to the pure materials.
|  | Things are generally complicated, but full of potential for custom tailored properties!
Questionaire
Multiple Choice questions to 2.1.2

© H. Föll (Advanced Materials B, part 1 - script)