# Q & A: negative Thomson effect

Most recent answer: 10/03/2013
Q:
why iron,cobalt show negative thomson effect.thanx
- rifat (age 19)
A:

This question is fun, because I never thought about the Thomson effect before. I can present some useful background, but not fully answer it. For readers like me who weren't sure what the Thomson effect is, it's an effect which makes a little piece of wire which is hotter at one end than the other either end heat up or cool down, depending on which way a current flows through it. That's in addition to the Joule heating that any wire with resistance R gets when a current, I, flows through it, with heating power I2R.

What causes the Thomson effect? Crudely, you can think of the electrical current as dragging some heat along. If more heat is dragged into an area than is dragged out, than the area will heat up. If the opposite occurs, it will cool down.

Let's start by describing the Seebeck coefficient, which describes how heat is dragged along with current in a material at uniform temperature. It's easiest for me to think about this in terms of entropy, a quantity that represents how many different states something can be in. Entropy increases as something gets hotter. Although the total amount of entropy isn't fixed, we can for the purpose of understanding the Thomson effect think of entropy as something that gets dragged one way or the other, since other effects give the net entropy increase. Which way is it dragged?

Let's start by trying to understand the effect in something simple, like a piece of silicon doped so that the current is carried by some free electrons, i.e n-type. Each electron can be in any of a large batch of otherwise empty states in a band, so it carries entropy. When current flows, the entropy gets dragged the same way the electrons go. That happens to be defined as a negative Seebeck coefficient.

Now let's think of p-type silicon. Here almost all the mobile electron states are filled, leaving just a few empty states, called "holes". Each hole can be in any one of a large batch of otherwise filled states in a band, so the holes carry entropy. Holes are missing electrons, so they have the opposite charge to electrons. They flow the opposite direction. The entropy will flow along with the holes, in the opposite direction to how it would flow if the current were carried by electrons. This is defined as a positive Seebeck coefficient.

What about metals? These have bands of electron states that are more or less halfway filled up. Unlike our simple cases above, it's not obvious whether adding more electrons increases or decreases the entropy. Depending on the details of how the state energy depends on the velocity ("band structure"), these can behave more like it is the electrons that carry the current or more like holes do. So that means you have to get deep into the details to even figure out the sign of the Seebeck coefficient.

OK, now to the Thomson coefficient. Will a little region that's hotter on one side than the other heat up or cool down as current flows say from the hot side to the cold side? That depends on whether the flow of entropy in from one side is bigger than or less than the flow out the other way. So it depends on how the Seebeck coefficient changes with temperature. That's even more complicated to calculate than what sign to expect for the Seebeck coefficient.

I don't know enough about those metallic band structures to know why different ones have positive or negative Thomson coefficients, except for some simple cases that don't include iron and cobalt. It's not surprising that they are similar, since both show similar magnetism, but they aren't the only metals with negative Thomson coefficients.

For nice articles on some of these effects, see   and  .

Mike W.

(published on 10/03/2013)