Layman's method to sharpen a wire (STM-tip) We use a platinum-irididum wire to fabricate our STM tips. And by "fabricate"
I mean to cut it with really sharp pliers or scissors.
Sometimes we get good tips but most of the time they are not usable especially
when you need a high aspect ratio and a sharp tip with preferably only "one atom"
where the tunneling current goes through.
Therefore my question:
How could one process a platinum-iridium wire to get a really sharp tip?
(Besides using chemicals to etch it)
Here are some characteristics of the pt80ir20 wire that we use: http://shjmjs.en.b2b168.com/shop/supply/13658861.html
The melting point is around 1800 ° C.
And by "sharp" and "high aspect ratio" I mean a geometry like this:

 A: I used an arc-welder to make thermocouples from wires like your starting materials. Your desired objective looks like some of my 'failures.' Try loading a wire in tension and then break it with an arc (i.e. heat and melt a short section.)  The ends might draw to the fine diameters you're trying to achieve. I'd try using one of the welders that are designed for making small thermocouples, they are common in labs, they are precise, and the arc is shielded with a stream of Ar to prevent contamination.
You likely have lots of unsuitable tips for many tries, but I don't expect you need lots of successe.
A: I would consider the possibility of using Focused Ion Beams.  Two papers on the process are found here:
Nanoscale Ion Beam Sculpting 
Focused Ion Beam Microscopy and Micromachining
The structures produced are to the right scale, although the papers talk about ~10 nm as being the current feasible limit. The second paper discuss ion beam milling and shows examples in copper (Cu) which has a melting point of 1984F, so certainly the temperature range won't be a problem.  The most obvious process would be to draw and cut the wire to at a scale where such an operation could be performed reliable, then use the ion beams to mill the tip to the desired size and shape. 
The other possibility is to build a mold or an extrusion die, and force the high nearly molten platinum-iridium through the copper hole. There would probably need to be an interim step in an extrusion process to provide some surface coating that would behave as a lubricant to prevent binding of the copper and platinum-iridium. One can imagine the process working as taking the rough wire, heating then forcing through the lubricant covered milled hole.  Allow to cool enough to harden, then extracting. Obviously very fine motor control would be needed, but presumably some of that technology is already mastered. 
