  We explore the thermoelectric properties of gold atomic chains bridging gold
electrodes by means of \textit{ab initio} and semi-empirical calculations, and
heuristic reasoning. We predict the thermoelectric voltage induced by a
temperature difference across such junctions to oscillate, repeatedly changing
sign, as a function of the number of atoms $N$ making up the atomic chain. We
also predict the amplitude of the oscillations to be proportional to $N$ for
long atomic chains. Further we predict the thermoelectric voltage to change
sign, in some cases, if the junction is stretched without changing $N$. Our
predictions apply regardless of whether regular or irregular electrode grain
boundaries are present and whether the electrodes are symmetric or asymmetric.
Our findings may pave the way to the realization of new mechanically
controllable voltage switches enabling direct conversion of heat into
electricity in energy harvesting applications.
