Constantan Negative Temperature Coefficient

[Jon86]

This is probably more of a physics based question, but how is it that constantan is the only metal with a negative temperature coefficient?
I kind of understand the physics behind metals increasing their resistance with temperature, so how come this specific alloy acts completely differently?

[Paul Price]

Constantin is not a metal element, but an alloy of metals. There are some metal elements that also have negative coefficients of resistance:

The electrical resistivities, rho , of Eu, Yb and Ba have been measured at high temperatures. In solid Yb and Ba rho varies linearly with temperature. This is contrary to some previous results. Both metals show a large percentage increase of rho on melting. The temperature dependence of rho in Eu is nonlinear and there is a smaller percentage change on melting. The resistivities of liquid Eu and Ba are larger than those of any other liquid metals. Negative temperature coefficients of resistivity are observed for all three metals in the liquid state. These results and those obtained in our earlier measurements on alloys of rare earth metals are discussed in the context of existing theories. Even in the liquid rare earth metals and their alloys an interpretation involving the liquid structure factors and the effective valences of the components may still provide a reasonable qualitative explanation of the behavior of the resistivity. The occurrence of negative temperature coefficients in other disordered metallic systems is also observed.

[rolycat]

Absent a competent physicist, I will have a crack at answering this.

First off, pure metals normally have a positive temperature coefficient of resistance (TCR), although as Paul Price has observed this is not always true for the liquid phase. As a matter of interest the paper from which he has quoted the bulk of his reply can be found here.

As you observed in your question constantan is an alloy, but it is not the only one with a negative TCR. Bismuth, for example, exhibits a negative TCR if just a tiny amount of tin is present.

Another point to consider is that the TCR is an approximation over a limited temperature range. The relative resistance change vs. temperature function deltaR/R = f(T) is primarily linear for pure conductors, but alloys such as nichrome and constantan have nonlinear functions. Consequently the TCR is defined as the slope of a chord joining two temperatures on the curve. Depending on the temperatures chosen the TCR may be positive or negative for a given alloy.

For constantan the proportions of copper and nickel were adjusted empirically until the TCR was close to zero at around room temperature.

The exact mechanism is not well understood, but in constantan the occupancy of the 3d and 4s electron shells in an alloy of copper and nickel at a 60:40 ratio provide a structure which just compensates for the increased scattering caused by rising temperature.

[Conrad Hoffman]

Low TCR, but watch out for the darn thermocouple effect! Thus the use of manganin for resistance standards, low TCR combined with low thermocouple voltage against copper, plus you can solder the stuff, unlike the "800" alloys that need to be spot welded.