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After doing some research on gold purity, I found that the current record of gold fineness is at an astounding 999.999 fine achieved by the Perth Mint, Australia 1957. However, I could not find any other attempts to break this record.

I have also read the other related answers like this one: Obtaining 100% pure metal

I was hoping that perhaps some insight could be given as to how the current fineness record was achieved, and what refinement or fineness verification barriers may need to be overcome to achieve finer purities.

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    $\begingroup$ And to what purpose? $\endgroup$
    – Karl
    Commented Apr 10, 2018 at 5:28
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    $\begingroup$ Ever heard of zone-refining? chemistry-desk.blogspot.co.uk/2012/08/zone-refining.html $\endgroup$
    – Waylander
    Commented Apr 10, 2018 at 7:56
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    $\begingroup$ My ion accelerator makes pure gold all the time - if an ion makes it down the beam line into the end station, it has mass 197 and charge 1. Now, getting a macroscopic amount takes something on the order of the Y-12 plant... $\endgroup$
    – Jon Custer
    Commented Apr 10, 2018 at 13:14

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There are many approaches that can be used to purify an element such as gold. Gold has a different melting point than any likely contaminant so zone refining can be used. Imagine a bar or rod of gold with some contaminant with a lower melting point than gold, melt one end of the bar then move the heated and molten zone the length of the bar, the atoms of the contaminant will be more likely to remain molten and not solidify, thus the contaminants with a lower melting point will move slightly towards the end that was molten last. If the procedure is repeated, then the gold in the bar will become more and more pure. Once all the lower melting point impurities have been reduced in concentration to an acceptable level, then the process is continued to move the gold away from the higher melting impurities and a section of the bar is selected to optimise the reduction in impurities.

Zone refining was first used commercially for semiconductor manufacturing; germanium was purified to 999.999999 purity, using the notation in the original question. I'm unsure of the utility of purifying gold to the level described above, apart from the 'we can do this' factor. You could possibly use a centrifuge and purify gold (III) fluoride in the gaseous state, although materials of construction would be a problem; it is very corrosive. There would also be hydrometallurgical techniques, but I don't know any chelating agents specific for gold.

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