Thoriated Tungsten filaments

This seems to be well described here, which, in turn contains a reference to L.W. Turner,(ed), Electronics Engineer's Reference Book, 4th ed. Newnes-Butterworth, London 1976. I just might have a copy of that somewhere, but not to hand.

The mechanism agrees with what I remember being told it was: Thorium is added to the Tungsten filament, and then the whole thing is heated significantly hotter than its normal working temperature. This causes (why?) the Thorium to migrate to the surface of the filament, resulting in essentially a Thorium-plated Tungsten filament. Thorium has a lower work-function than Tungsten so the effective work-function of the filament is that of Thorium.

It should be fairly easy to convince yourself, based on the activity of Thorium compared with the number of electrons a hot cathode needs to emit, that its radioactivity can't be a factor.

I am not sure why Thorium is not just plated onto the filament, although I expect this is to make production simpler: if you can effectively plate the filament by heating it after production (which you can do electrically of course, since that's what you do anyway) then this makes it all cheaper and easier. Probably the initial heating of the thing also helps weed out infant mortality: filaments which are going to fail early probably fail during the initial heating.

It's actually thorium oxide ("thoria"), by itself an insulator, that is added to the tungsten. Though it is, in fact, the metallic thorium film, a monolayer adsorbed at the surface, that is responsible for the reduction of the work function. Simply because thorium has a lower work function than tungsten does: 3.4 vs. 4.5 eV.

Or put another way… The Fermi level of thorium is higher than tungsten's, thus closer to the energy of free electrons in vacuum. As the electrons in the tungsten bulk and in the thorium surface layer are in equilibrium, their Fermi levels are… well, level. This means there is a contact potential across the interface, but, much more importantly, it makes it easier for the electrons to escape. The thorium monolayer thus lowers the energy barrier that the electrons need to overcome in order to make it to the free vacuum state.

Thermionic emission is thermally activated: Only the outliers among the conduction electrons, in terms of their distribution of kinetic energy, make it across the barrier. So the deceivingly small difference between 3.4 and 4.5 eV is actually a big deal, given that the average thermal energy is maybe 0.1 or 0.2 eV, depending on operating temperature.

The operating temperature is the issue, however. If it were just about the work function, we'd just use pure thorium, all the way. Or any old metal, really, as long as its work function is low. Of which there are many, compared to tungsten.

When it comes to thermionic emitters, though, there are always two competing effects. Increasing the temperature means more electrons are "evaporated", make it into the vacuum. But the surface atoms themselves also evaporate. They detach from the emitter and end up God/Newton knows where in the vacuum chamber.

At a temperature that would produce an appreciable electron current, thorium atoms evaporate all too easily. If it were bulk thorium, it wouldn't last long. But when dissolved into tungsten, only part of the surface is covered by thorium at any given time. And when it evaporates, which it does, the partial layer is replenished via diffusion from the bulk.

That's the trick to it. I doubt that there's a theoretical explanation based on "first principles" alone. After all, that would involve band-structure calculations, interface bonding, atomic evaporation, as well as computations of diffusion coefficients through the bulk, along grain boundaries, and across the surface. Irving Langmuir, back in 1934, sure tried to provide that theoretical base, in "Thoriated tungsten filaments", but ultimately it just works in practice.

The (weak) radioactivity of thorium is an unfortunate side effect. Though all it does is reduce the viability of thoriated tungsten in commercial applications.