Surface science experiments very often start with atomically smooth crystal surfaces as substrates. After one experiment ends the surface is sputter cleaned with cycles of keV energy argon ions alternated with moderate thermal anneals of the local surface damage induced by the ions to recover a crystalline surface.
However newly manufactured crystal substrates are diced with a saw from a large crystal than abrasively ground only to optical or "mirror-smoothness" with roughness of the order of 100 Å rms. For a typical metal fcc(111) surface that may be 40 monolayers rms.
Thermal anneals can produce local atomic smoothness such that surface states appear in angle resolved photoemission spectroscopy (ARPES) but since these can occur on vicinal surfaces with several degrees of miscut from (111) they don't require planarity. In these cases low energy electron diffraction (LEED) patterns confirm the absence of any single well-defined crystal plane.
Thus for new samples whose surfaces are still rough at tens of monolayers, a higher temperature anneal may be required in order to induce "surface melting" or at least high mobility of the atoms at the surface in order for them to move distances of the order of microns and "fill in" the valleys and reduce the peaks, with the ultimate goal of establishing large areas of atomic planarity with an acceptable density of individual step edges consistent with the global surface miscut from the target crystal plane.
In order to understand roughly what temperature will be necessary to "melt the surface" and achieve atomic planarization of this mechanically ground metal surface, I'd like to understand better:
Question: What are the basic principles (and vocabulary1) necessary to begin modeling2 the rate of atom surface diffusion and thermal planarization of rough metal surfaces?
1Answers to the "vocabulary" bit will help me to pursue further reading on my own.
2Since "melting the mountains and filling in the lakes" requires vicinal surface diffusion I'm afraid this will be challenging to model with a simple ad hoc program, even in 1D, but I would like to try. Perhaps there are surface energies for various surfaces that I can use in a simple model to estimate mobilities and therefore an approximate time vs temperature plot. We obviously don't want to melt the bulk or get even close to that, but I think "surface melting" concept applies here.
I think that the thermally-induced relaxation and planarization of nanofabricated artificial structures on metal surfaces has been studied in the past (gold is especially mobile in this regard) but that was decades ago and so far I can't find evidence of that line of research in the literature because I simply haven't found the right combinations of terms of the era to search for. See for example the (currently unanswered) question in Physics SE "half-life" of a holographic grating imprinted on gold?