I Why are the crystallographic direction indices u,v, and w?

[Stenny]

Why are the crystallographic direction indices u,v, and w? And as an add on, why are the miller indices h,k, and l? Why did we pick these letters for each? I’m having a tough time remembering which letters to use and some context might help.

 

[pines-demon]

This would go into the history of science forum if we had one. Let me see what I can look up about this.

 

[dextercioby]

There's no secret or specific meaning behind 'h,k,l'. They were adopted by Miller in his 1839 treatise on crystallography from an article by Whewell from 1825.

As for 'u,v,w' there's also no relevant meaning to them, they are the closest to 'x,y,z'. Before QM, crystallography was foremost geometry, so one had to use a huge apparatus of letters to distinguish things.