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Pure metals are rarely used - in the
real world you use alloys. |
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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: |
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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. |
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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. |
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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) |
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This formula is a special case of
Nordheims
rule which states . |
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| r » XA ·
rA + XB
· rB + const. ·
XA ·XB |
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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. |
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If you have intermetallic compounds in your phase diagram, use
Nordheim's rule with the intermetallic phases as XA
and XB. |
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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. |
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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. |
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You will have to turn to superconductors (forgetting about cost
considerations), if you can't live with Ag. |
© H. Föll (Electronic Materials - Script)
