Interesting, apparently most of the green quartz you see for sale is manufactured. It's called "CHromium Quartz". Regular clear quartz that has been treated in China to undergo a transformation into the Green style. Secondary fuzzy crystal grow on the side and base during this process.
"Green quartz can be produced in the lab by a modification of the process used to manufacture large, high-quality quartz crystals for electronics applications. The process involves heating the quartz with water under high pressure. This causes the quartz to recrystallize. If other substances are present these might be included into the new crystals. For example inclusion of chromium can result in deep green quartz. So, existing quartz clusters (often with damaged crystals tips because these clusters are essentially worthless) are heated with water under high pressure, producing clusters with new deep green tips. These tips have a characteristic etched or stepped growth pattern. The material is lab-grown and not produced in any mine, despite what some dealers might want you to believe."
Dark green tips with fuzzy new growth on the sides-
Here is natural "Prasem" Green Quartz for comparison-