I have a technical question here re: gemstones in The Stormlight Archive. How are the lines drawn between different types of gem? Emerald and Heliodor are both varieties of the mineral beryl. Emerald can get its color from trace amounts of chromium, vanadium and/or iron. Heliodor gets its color from iron combined with microscopic crystal defects. So, is the line between these two defined by color? If so, would a heliodor lose its usefulness if it were heated (which would turn it colorless or pale blue). Is it defined by trace elements--in which case, how do you deal with emeralds, or with aquamarine (the blue variety of beryl, which can also contain chromium or vanadium in small quantities and is mostly colored by iron). Sorry for getting so technical, but this gem nerd needs to know!
I actually spent a long time working on this while building the world. You'd probably be amused by how long I spent on it. Chemically, many of them are actually very similar, as you pointed out. I tried doing the book originally with them all being different, not using any that were basically the same crystal with different colors, but it didn't work out. There weren't enough, and so I had to stretch to make it all work.
So, I went back to the original, and decided that color was enough to differentiate them. Just as steel and iron are very similar in the mistborn world, Emerald and Heliodor can be very similar--but produce different effects. The idea here is that the physical items (like the metals or the crystals) provide a key by which magical interaction occurs.
So, in a long winded answer, a gemstone with an impure color would be considered like a bad alloy in the Mistborn magic--it either wouldn't work at all, or would work very poorly. The chemical and color signature needs to be of a specific variety to provide the proper key to accessing the power of transformation.