This is fluorite, a wonderful mineral that is only rarely cut as gemstones. Natural fluorite has an incredible range of colors, not just purple and green but reds, yellows, blues, and more. On top of that, fluorite can have strong fluorescence. In fact, it can be so strong that fluorescence is named after fluorite.
Natural specimens from the Blue John mine are known to change colors in sunlight because of their strong blue fluorescence, and this phenomenon attracted the interest of scientists. It was discovered that trace rare earths - particularly europium - are responsible for this wonderful glow.
This Europium-doped fluorite is grown for science - these crystals are valuable because they are extremely sensitive to many kinds of radiation (not just UV), so can be used as 'scintillators' for detecting the presence of x-rays. Eu:Fluorite's glow is strong enough to change its color in direct sunlight.
You might be wondering "why is fluorite jewelry is so rare when it's so cool?" That's because fluorite is a really tricky material to cut. It has low Moh's hardness (rank 4 on the scale), and on top of that has four perfect cleavage planes - it wants to break into perfect octahedrons. Combined with one of the lowest refractive indexes of any gem, it requires special designs and extreme care when cutting - not for the faint of heart. Even pinching the stone too hard when bending the silver prongs can make it decide to start cleaving (as we learned to our dismay).
But, despite how hard it is to cut and set these, I think the incredible blue glow makes it all worthwhile! While the pendants need to be worn with a bit of extra care, the amazing change in color going from inside to outside is absolutely fantastic.
