| ||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) |
| || ||
| || ||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
| ||Lets look at some examples: |
|| Complete miscibility
| Miscibility gap |
phase diagram in the link.
| Intermetallic phases |
| || |
| ||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! |
| || || |
| || ||
© H. Föll (Advanced Materials B, part 1 - script)